Physics Test 3
RRB18. The angular speed of the minute hand of a watch is: A. (π/1800) rad/s B. (π/60) m/s C. (π/30) m/s D. (2π) m/s E. (60) m/s
(π/1800) rad/s
COM14. Cart A, with a mass of 0.2 kg, travels on a horizontal air track at 3 m/s and hits cart B, which has a mass of 0.4 kg and is initially at rest. After the collision the center of mass of the two cart system has a speed in m/s of: A. zero B. 1.0 m/s C. 2.3 m/s D. 2.5 E. 5.0 m/s
1
E16. The uniform rod shown below is held in place by the rope and wall. Suppose you know the weight of the rod and all dimensions. Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point: A. 4 B. 3 C. 2 D. 1, 2, or 3 E. 1
2
TAM19. Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia I and is spinning with angular velocity ω . The second disc has rotational inertia 2 I and is spinning in the same direction as the first disc with angular velocity 2 ω as shown. The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of: A. 5ω /3 B. sqrt 3 C. w sqrt 7/3 D. ω E. 3ω
A. 5ω /3
COM4. The center of mass of a system of particles has a constant velocity if: A. the forces exerted by the particles on each other sum to zero B. the external forces acting on particles of the system sum to zero C. the velocity of the center of mass is initially zero D. the particles are distributed symmetrically around the center of mass E. the center of mass is at the geometric center of the system
B. the external forces acting on particles of the system sum to zero
RRB8. The amount of work done on a rotating body can be expressed in terms of the product of A.force and time of application of the force. B. torque and angular displacement. C. force and lever arm. D. torque and angular acceleration. E. torque and angular velocity.
B. torque and angular displacement.
COM3. A thick uniform wire is bent into the shape of the letter "U" as shown. Which point indicates the location of the center of mass of this wire? A. A B. B C. C D. D E. E
B
Q2. Two points, A and B are on a disk that rotates about an axis. Point A is two times further from the axis as point B. If the speed of B is v, what is the speed of A? A.v B.2v C.v/2 D.4v E.v/4
B.2v because v=rw
Q1: When a thin uniform disk of mass M and radius R is rotated about it's center the moment of inertia is ½MR2. When rotated about a parallel axis at it's rim it's moment of inertia is: A.2MR^2 D. 3MR^2/4 B.3MR^2/2 E. MR^2 C.MR^2/2
B.3MR^2/2
Q2: A net torque applied to a rigid object always tends to produce A.linear acceleration B.angular acceleration C.rotational inertia D.rotational equilibrium
B.angular acceleration. because torque = I (angular acceleration)
Q4. A disk rolls without slipping at a constant speed on level ground. Its rotational kinetic energy is A. ¼ K translation D. 2 K translation B.½ K translation E. 4 K translation C.Equal to K translation
B.½ K translation
E10. The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE) and friction between the rod and the wall. To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for computing torque? A. A B. B C. C D. D E. E
C
RRB32. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML 2/12. When pivoted about a parallel axis through one end, its rotational inertia is: A. ML^2/12 B. ML^2/6 C. ML^2/3 D. 7ML^2/12 E. 13ML^2/12
C. ML^2/3
RRB41. A small disk of radius R 1 is mounted coaxially with a larger disk of radius R 2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top,as shown in the overhead veiw below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force ¢ as shown. The acceleration of the block is: A. R1F/mR2 B. R1R2F/(I - mR2^2) C. R1R2F/(I + mR2^2) D. R1R2F/(I - mR1R^2) E. R1R2F/(I + mR1R^2)
C. R1R2F/(I + mR2^2)
RRB5. Which of the following statements about the motion of the second hand of a clock is true? A. The tangential velocity of the tip is constant. B. The tangential acceleration is nonzero. C. The angular acceleration is zero. D. The radial acceleration is zero. E. The angular velocity is zero.
C. The angular acceleration is zero.
RRB13. Starting from rest at the same time, a coin and a ring roll down an incline without slipping. Which reaches the bottom first? A. The winner depends on the relative masses of the two. B. The winner depends on the relative diameters of the two. C. The coin reaches the bottom first. D. They arrive at the bottom simultaneously. E. The ring reaches the bottom first.
C. The coin reaches the bottom first.
TAM28. If the angular momentum of a system is constant, which of the following statements must be true? A. A constant torque acts on each part of the system. B. Zero net torque acts on each part of the system. C. Zero net torque acts on the system. D. No torque acts on any part of the system. E. A constant external torque acts on the system.
C. Zero net torque acts on the system.
RRB4. A wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude? A. v, tangential velocity B. a, radial acceleration C. a, tangential acceleration D. w, angular velocity E. All of these are correct.
C. a, tangential acceleration
E1. A net torque applied to a rigid object always tends to produce: A. linear acceleration B. rotational equilibrium C. angular acceleration D. rotational inertia E. none of these
C. angular acceleration
T1. A uniform disk rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is A. twice its translational kinetic energy B. one fourth its translational kinetic energy C. half its translational kinetic energy D. four times its translational kinetic energy E. the same as its translational kinetic energy
C. half its translational kinetic energy
TAM3. Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is: A. less than half the angular velocity of wheel 1 B. more than twice the angular velocity of wheel 1 C. half the angular velocity of wheel 1 D. twice the angular velocity of wheel 1 E. the same as the angular velocity of wheel 1
C. half the angular velocity of wheel 1
TAM11. A single force acts on a particle situated on the positive x axis. The torque about the origin is in the negative z direction. The force might be: A. in the positive x direction B. in the negative x direction C. in the negative y direction D. in the positive z direction E. in the positive y direction
C. in the negative y direction
Q5. If both the mass and speed of an object are doubled, its momentum A. remains unchanged B. is doubled C. is quadrupled D. decreased
C. is quadrupled
E20. A body is in translational equilibrium when A. it is acted on by a constant force. B. it has a constant acceleration. C. it has a constant velocity. D. no contact forces are involved. E. no friction forces are involved.
C. it has a constant velocity.
COM20.An elastic collision is one in which: A. momentum is not conserved but kinetic energy is conserved B. total mass is not conserved but momentum is conserved C. kinetic energy and momentum are both conserved D. momentum is conserved but kinetic energy is not conserved E. the total impulse is equal to the change in kinetic energy
C. kinetic energy and momentum are both conserved
TAM24. For a disc of mass M and radius R that is rolling without slipping, which is greater, its translational or its rotational kinetic energy? A. The answer depends on the mass. B. Its translational kinetic energy is greater. C. They are equal. D. The answer depends on the radius. E. Its rotational kinetic energy is greater.
B. Its translational kinetic energy is greater.
E9. Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods. Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod? A. Only 2 B. Only 3 C. Only 1 D. All three E. Only 1 and 2
B. Only 3
TAM32. A woman sits on a spinning piano stool with her arms folded. When she extends her arms, which of the following occurs? A. She increases her moment of inertia, thereby increasing her angular speed. B. She increases her moment of inertia, thereby decreasing her angular speed. C. She decreases her moment of inertia, thereby decreasing her angular speed. D. She decreases her moment of inertia, thereby increasing her angular speed. E. Both her moment of inertia and her angular speed remain constant.
B. She increases her moment of inertia, thereby decreasing her angular speed.
E13. A ladder leans against a wall. If the ladder is not to slip, which one of the following must be true? A. The coefficient of friction between the ladder and the wall must not be zero B. The coefficient of friction between the ladder and the floor must not be zero C. Both A and B D. Either A or B E. Neither A nor B
B. The coefficient of friction between the ladder and the floor must not be zero
RRB39. A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is: A. applied tangentially halfway between the axis and the rim B. applied tangentially at the rim C. applied radially halfway between the axis and the rim D. applied radially at the rim E. applied at the rim but neither radially nor tangentially
B. applied tangentially at the rim
COM2. The center of mass of the system consisting of Earth, the Sun, and the planet Mars is: A. closer to the Earth than to either of the other bodies B. closer to the Sun than to either of the other bodies C. closer to Mars than to either of the other bodies D. at the geometric center of the triangle formed by the three bodies E. at the center of the line joining the Earth and Mars
B. closer to the Sun than to either of the other bodies
RRB31. To increase the rotational inertia of a solid disk about its axis without changing its mass: A. drill holes near the rim and put the material near the axis B. drill holes near the axis and put the material near the rim C. drill holes at points on a circle near the rim and put the material at points between the holes D. drill holes at points on a circle near the axis and put the material at points between the holes E. do none of the above (the rotational inertia cannot be changed without changing the mass)
B. drill holes near the axis and put the material near the rim
TAM27. A disc rotates clockwise in the plane of the page. What is the direction of the angular momentum vector? A. angular momentum has no direction B. into the page C. clockwise D. counterclockwise E. out of the page
B. into the page
TAM17. When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy: A. must increase B. must decrease C. must remain the same D. may increase or decrease depending on her initial angular velocity E. tilts away from the vertical
B. must decrease
COM16. A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The average force on the club on the ball during the time T is: A. mvT B. mv/T C. (1/2)mv2T D. mv2/(2T) E. mT2/(2v)
B. mv/ T
RRB9. A wagon wheel consists of 8 spokes of uniform diameter, each of mass m s and lengthL cm. The outer ring has a mass m ring. What is the moment of inertia of the wheel? Assume that each spoke extends from the center to the other ring and the ring is of negligible thickness. A. (8/3 m + 1/4 m(ring) ) L^2 B. (8/3 m + 1/2 m(ring) ) L^2 C. ( m(ring) ) L^2 D. (8/3 m + m(ring) ) L^2 E. (1/3 m + m(ring) ) L^2
D. (8/3 m + m(ring) ) L^2
COM24. Two students, sitting on frictionless carts, push against each other. Both are initially at rest and the mass of student 1 and the cart is M, and that of student 2 and the cart is 1.5M. If student 1 pushes student 2 so that she recoils with velocity what is the velocity of student 2. A. - 2/3 v B. + 1.5 v C. -1.5 v D. + 2/3 v E. v
D. +2/3 v
TAM30. A spinning bicycle wheel is supported as shown by a line fastened to one end of its axle. The resultant torque acting on the wheel lies along which of the following axes? A. x B. -y C. z D. -z E. y
D. -z
Two objects, one of mass m 1 = 2 kg and the second of unknown mass, are connected by a compressed spring with negligible mass. The system is at rest on a frictionless table. Both objects are released simultaneously. m 1 is observed to recoil with velocity and m 2 shots forward with velocity What is the mass of m 2? A. 0.5 kg B. 4 kg C. cannot be determined D. 1 kg E. 2 kg
D. 1 kg
A boy and girl on ice skates face each other. The girl has a mass of 20 kg and the boy has a mass of 30 kg. The boy pushes the girl backward at a speed of 3.0 m/s. As a result of the push, the speed of the boy is A. 3.0 m/s B. 9.0 m/s C. 4.5 m/s D. 2.0 m/s E. zero
D. 2.0 m/s
T10. A pulley of radius 0.10 m and having a moment of inertia of 0.30 kg-m2 has a cord wrapped around it and attached to a 6.0 kg mass as shown. The pulley is free to rotate about a fixed axis through its center. The mass is allowed to fall from rest. What is the speed of the mass after it has fallen 2.0 m? A. 1.8 m/s B. 4.4 m/s C. 6.5 m/s D. 2.6 m/s E. 5.1 m/s
D. 2.6 m/s
E12. A picture P of weight W is hung by two strings as shown. The magnitude of the tension force of each string is T. The total upward pull of the strings on the picture is: A. 2W cos θ B. T sin θ C. T cos θ D. 2T sin θ E. 2T cos θ
D. 2T sin θ
TAM23. You are given two hoops ( I = mR 2), which are (1) brass and (2) wood, and two cylinders ( I = mR 2), which are (3) brass and (4) wood; each has radius R. If all are released from the same starting line at the same time, the one(s) that reach the bottom first are A. 1 and 2 B. 1, 2, 3, and 4 C. 1 D. 3 and 4 E. 3
D. 3 and 4
COM8. A 1.0 kg-ball moving at 2.0 m/s perpendicular to a wall rebounds from the wall at 1.5 m/s. The change in the momentum of the ball is: A. zero B. 0.5 N ⋅ s away from wall C. 0.5 N ⋅ s toward wall D. 3.5 N ⋅ s away from wall E. 3.5 N ⋅ s toward wall
D. 3.5 N per s away from wall
COM22. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped piece is A. 1 B. 2 C. 3 D. 4 E. 5
D. 4
RRB28. The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is: A. MR2^2 B. ML^2/2 C. ML^2 D. MR^2 E. none of these
D. MR^2
RRB1. Two points, A and B, are on a disk that rotates about an axis. Point A is closer to the axis than point B. Which of the following is not true? A. Point B has the greater speed. B. Point A has the lesser centripetal acceleration. C. Points A and B have the same angular acceleration. D. Point B has the greater angular speed. E. Point A has the lesser tangential acceleration.
D. Point B has the greater angular speed.
E21. The horizontal bar in the figure will remain horizontal if A. L1 = L2 and R1 = R2 B. L1M1 = L2M2 C. L1 = L2 and M1 = M2 D. R1 = R2 and M1 = M2 E. R1L1 = R2L2
D. R1 = R2 and M1 = M2
RRB14. For a hoop (ring) of mass M and radius R that is rolling without slipping, which is greater, its translational or its rotational kinetic energy? A. Its translational kinetic energy is greater. B. Its rotational kinetic energy is greater. C. The answer depends on the mass. D. They are equal. E. The answer depends on the radius.
D. They are equal.
COM9. If the total momentum of a system is changing: A. particles of the system must be exerting forces on each other B. the system must be under the influence of gravity C. the center of mass must have constant velocity D. a net external force must be acting on the system E. none of the above
D. a net external force must be acting on the system
RRB34. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by: A. applying the force near the axle, radially outward from the axle B. applying the force near the rim, radially outward from the axle C. applying the force near the axle, parallel to a tangent to the wheel D. applying the force at the rim, tangent to the rim E. applying the force at the rim, at 45° to the tangent
D. applying the force at the rim, tangent to the rim
Q1. Your friend says that impulse equals momentum. This statement isn't correct, and the missing word is A. work. B.acceleration. C.speed or velocity. D. change.
D. change.
COM13. Force: A. equals the negative integral (with respect to distance) of the potential energy function B. is the ability to do work C. is the rate of change of doing work D. equals the time rate of change of momentum E. has dimensions of momentum multiplied by time
D. equals the time rate of change of momentum
RRB36. τ = Iα for an object rotating about a fixed axis, where τ is the net torque acting on it, I is its rotational inertia, and α is its angular acceleration. This expression: A. is the definition of torque B. is the definition of rotational inertia C. is the definition of angular acceleration D. follows directly from Newton's second law E. depends on a principle of physics that is unrelated to Newton's second law
D. follows directly from Newton's second law
TAM26. A wheel is rotating clockwise on a fixed axis perpendicular to the page ( x). A torque that causes the wheel to slow down is best represented by the vector A. 1 B. 2 C. 3 D. 4 E. 5
A. 1
TAM4. A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is: A. 1 B. 2 C. 3 D. 1/2 E. 1/3
A. 1
COM18. A 4.0-N puck is traveling at 3.0 m/s. It strikes an 8.0-N puck, which is stationary. The two pucks stick together. Their common final speed is: A. 1.0 m/s B. 1.5 m/s C. 2.0 m/s D. 2.3 m/s E. 3.0 m/s
A. 1 m/s
RRB11. A homogeneous solid cylinder of mass m, length L, and radius R rotates about an axis through point P, which is parallel to the cylinder axis. If the moment of inertia about the cylinder axis is 1/2 mR^2, the moment of inertia about the axis through P is A. 1.5mR^2 B. mR^2 C. 1/2 mR^2 D. 0.4mR^2 E. 2/3 mR^2
A. 1.5mR^2
T3. Dan and Jane are playing on a seesaw with their mother in a park. The 6.0 m long uniform board is hinged at its midpoint. If Dan and Jane have masses of 30 kg and 20 kg and sit at distances of 2.0 m and 3.0 m respectively, calculate where their 60 kg mother should sit on the other side of the fulcrum for them to be in static equilibrium. A. 2.0 m B. 1.0 m C. 3.0 m D. 1.5 m E. 2.5 m
A. 2.0 m
A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s. Immediately after the collision the velocity of the system is A. 2.0 m/s to the right. B. -2.0 m/s to the right. C. 4.4 m/s to the right. D. 0 m/s E. 10 m/s to the right.
A. 2.0 m/s to the right
COM21. Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinectic energy of 50 J and Y has a kinetic erengy of: A. 20 J B. 8 J C. 310 J D. 125 J E. 50 J
A. 20 J
T7. You are pedaling a bicycle at 10 m/s. The radius of a wheel is 50 cm. The angular velocity of rotation of the wheel is A. 20 rad/s B. 3.2 rad/s C. 5.0 rad/s D. 6.3 rad/s E. 2.0 rad/s
A. 20 rad/s
COM6. Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 60-kg boy will have moved what distance? A. 4 m B. 5 m C. 6 m D. 10 m E. need to know the forces they exert
A. 4m
T8. A window washer attempts to lean a ladder against a frictionless wall. He finds that the ladder slips on the ground when it is placed at an angle of less than 75° to the ground but remains in place when the angle is greater than 75°. The coefficient of static friction between the ladder and the ground: A. depends on the mass of the ladder B. is about 1.3 C. is about 0.27 D. is about 0.13 E. depends on the length of the ladder
D. is about 0.13
TAM7. Possible units of angular momentum are: A. kg⋅m/s B. kg⋅m^2/s2 C. kg⋅m/s2 D. kg⋅m^2/s E. none of these
D. kg⋅m^2/s
COM17. An inelastic collision is one in which: A. momentum is not conserved but kinetic energy is conserved B. total mass is not conserved but momentum is conserved C. neither kinetic energy nor momentum is conserved D. momentum is conserved but kinetic energy is not conserved E. the total impulse is equal to the change in kinetic energy
D. momentum is conserved but kinetic energy is not conserved
RRB27. Three identical balls, with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. (2M is in the middle and 3M is the far right) The rotational inertia about the left end of the rod is: A. ML^2/2 B. ML^2 C. 3 ML^2/2 D. 6 ML^2 E. (7/2) ML^2
E. (7/2) ML^2
RRB33. The rotational inertia of a solid uniform sphere about a diameter is (2/5) MR 2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is: A. MR^2 B. (2/5)MR^2 C. (3/5)MR^2 D. (5/2)MR^2 E. (7/5)MR^2
E. (7/5)MR^2
COM25. Two students, sitting on frictionless carts, push against each other. Both are initially at rest and the mass of student 1 and the cart is M, and that of student 2 and the cart is 1.5M. If student 1 pushes student 2 so that she recoils with velocity what is the change in momentum of the two students? A. + 2/3 v B. + 2.5 v C. - 2/3 v D. - 2.5 v E. 0
E. 0
Momentum is conserved in which of the following? A. elastic collisions B. inelastic collisions C. explosions D. collisions between automobiles E. All of these are correct.
E. All of these are correct.
RRB15. For a disc of mass M and radius R that is rolling without slipping, which is greater, its translational or its rotational kinetic energy? A. Its rotational kinetic energy is greater. B. The answer depends on the mass. C. The answer depends on the radius. D. They are equal. E. Its translational kinetic energy is greater.
E. Its translational kinetic energy is greater.
RRB12. Two masses M and m ( M > m) are hung over a disc ( I disc = M' R 2) and are released so that they accelerate. If T 1 is the tension in the cord on the left and T 2 is the tension in the cord on the right, then A. T2 < T1 B. T2 = Mg/m C. T2 = Mg D. T1 = T2 E. T2 > T1
E. T 2 > T 1
E19. An object has the following two conditions, sum of F = 0 and sum of torque = 0. Which of the following statements can be true? A. The object is at rest. B. The object is moving at a constant velocity, and rotating with a constant angular velocity. C. The object is moving at a constant velocity but it not rotating. D. The object does not have a translation motion but is rotating at a constant angular velocity. E. all of the above
E. all of the above
RRB38. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according the their angular velocities after a given time t, LEAST TO GREATEST.
hoop, disk, sphere
E8. A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is: A. in stable equilibrium B. in unstable equilibrium C. in neutral equilibrium D. not in equilibrium E. none of the above
A. in stable equilibrium
TAM25. A torque is applied to a bolt by hanging a weight w from the end of the wrench, as shown. The coordinate axis along which the torque vector is directed is A. -x B. x C. -y D. y E. z
A. -x
TAM33. Two identical cylindrical discs have a common axis. Initially one of the discs is spinning. When the two discs are brought into contact, they stick together. Which of the following is true? A. The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value. B. The total angular momentum is unchanged, and the total kinetic energy is reduced to one-quarter of its original value. C. The total angular momentum is reduced to half its original value, but the total kinetic energy is unchanged. D. The total kinetic energy and the total angular momentum are unchanged from their initial values. E. Both the total kinetic energy and the total angular momentum are reduced to half of their original values.
A. The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value.
E2. The conditions that the sum of forces and the sum of the torques both vanish: A. hold for every solid body in equilibrium B. hold only for elastic solid bodies in equilibrium C. hold for every solid body D. are always sufficient to calculate the forces on a solid object in equilibrium E. are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic
A. hold for every solid body in equilibrium
TAM5. A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, least to greatest. A. hoop, disk, sphere B. sphere, disk, hoop' C. disk, hoop, sphere D. hoop, sphere, disk E. sphere, hoop, disk
A. hoop, disk, sphere
RRB3. Two objects, m 1 and m 2, both of mass m, are place on a horizontal platform which is rotating at a constant angular velocity. m 1 = m is located at a distance R from the axis of rotation and the second object of mass m 2 = 2m is located at a distance 2 R. The angular velocity of mass m 1____ to the angular velocity of m 2. A. is equal to B. unable to tell C. is less than D. depends how fast it is rotating E. is greater than
A. is equal to
COM11. A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion: A. is the same as the momentum of the projectile immediately before the explosion B. has been changed into kinetic energy of the fragments C. is less than the momentum of the projectile immediately before the explosion D. is more than the momentum of the projectile immediately before the explosion E. has been changed into radiant energy
A. is the same as the momentum of the projectile immediately after this explosion
COM5. The center of mass of a system of particles remains at the same place if: A. it is initially at rest and the external forces sum to zero B. it is initially at rest and the internal forces sum to zero C. the sum of the external forces is less than the maximum force of static friction D. no friction acts internally E. none of the above
A. it is initially at rest and the external forces sum to zero
A bullet of mass m and velocity "u" strikes and becomes imbedded in a wooden block of mass M, which is initially at rest on a frictionless surface. The ratio of the velocity of the system after collision to the initial velocity of the bullet is A. m/(m + M) B. M/(m - M) C. (M + m)/m D. M/(m + M) E. (M + m)/M
A. m/(m+M)
TAM15. A pulley with radius R is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. Mass m 1 is attached to one end and mass m 2 is attached to the other. The portion of the string attached to m 1 has tension T 1 and the portion attached to m 2 has tension T 2. The magnitude of the total external torque, about the pulley center, acting on the masses and pulley, considered as a system, is given by: A. m1 - m2gR B. (m1 + m2)gR C. m1 - m2gR + (T1 + T2)R D. (m1 + m2)gR + (T1 - T2)R E. m1 - m2gR + (T2 - T1)R
A. m1 - m2gR
In any and all collisions of short duration and for which it is true that no external forces act on the collision participants, A. momentum is conserved. B. the relative velocities before and after impact are equal and oppositely directed. C. kinetic energy is conserved. D. both momentum and kinetic energy are conserved. E. neither momentum nor kinetic energy is conserved.
A. momentum is conserved.
E18. A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted on the beam by the hinge has a vertical component that must be: A. nonzero and up B. nonzero and down C. nonzero but not enough information given to know whether up or down D. zero E. equal to W
A. nonzero and up
A particle of mass 2 m is moving to the right in projectile motion. At the top of its trajectory, an explosion breaks the particle into two equal parts. After the explosion, one part falls straight down with no horizontal motion. What is the direction of the motion of the other part just after the explosion? A. up and to the right B. straight up C. down and to the right D. stops moving E. up and to the left
A. up and to the right
TAM10. A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. A block of mass m 1 is attached to one end and a block of mass m2 , is attached to the other. At one time the block with mass m 1 is moving downward with speed v. If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley center, of the blocks and pulley, considered as a system, is given by: A. (m1 - m2)vR + Iv/R B. (m1 + m2)vR + Iv/R C. (m1 - m2)vR - Iv/R D. (m1 + m2)vR - Iv/R E. none of the above
B. ( m 1 + m 2) vR + Iv/ R
E7. A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is: A. in stable equilibrium B. in unstable equilibrium C. in neutral equilibrium D. not in equilibrium E. none of the above
B. in unstable equilibrium
TAM6. A hoop rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is: A. half its translational kinetic energy B. the same as its translational kinetic energy C. twice its translational kinetic energy D. four times its translational kinetic energy E. one-third its translational kinetic energy
B. the same as its translational kinetic energy
TAM29. The angular momentum of a system is conserved only if A. the sum of the internal torques is zero. B. the sum of the external torques is zero. C. the sum of the external torques equals the sum of the internal torques. D. the angular velocity is a function of time. E. the moment of inertia of the system is constant.
B. the sum of the external torques is zero.
T4. Two balls of putty have the same mass and initially one ball is at rest while the other is in motion with speed vo. They undergo a completely inelastic head-on collision and stick together. In terms of the initial kinetic energy, Ko, how much kinetic energy is lost due to the collision? A. (1/4) Ko B. (1/2) Ko C. (7/8) Ko D. (3/4) Ko E. All Ko is lost
B. (1/2) Ko
TAM9. A uniform disk has radius R and mass M. When it is spinning with angular velocity ω about an axis through its center and perpendicular to its face its angular momentum is Iω . When it is spinning with the same angle velocity about a parallel axis a distance h away its angular momentum is: A. Iω B. (I + Mh^2)ω C. (I - Mh^2)ω D. (I + MR^2)ω E. (I - MR^2)ω
B. (I + Mh^2)ω
COM12. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is: A. -mv B. -Mv/m C. -mv/M D. -v E. mv/M
B. -mv/M
COM10. Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5 m/s. The final recoil speed of A is: A. zero B. 0.38 m/s C. 0.5 m/s D. 0.67 m/s E. 1.0 m/s
B. 0.38 m/s
RRB25. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is: A. 1 B. 2 C. 1/2 D. 4 E. 1/4
B. 2
RRB43. For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is: A. 1 B. 2 C. 1/2 D. 4 E. 1/4
B. 2
RRB44. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is: A. 1 B. 2 C. 1/2 D. 4 E. 1/4
B. 2
RRB7. A cylinder ( I = mR^2) rolls along a level floor with a speed v. The work required to stop this cylinder is A. 1/4 mv^2 B. 3/4 mv^2 C. 1.25 mv^2 D. mv^2 E. 1/2 mv^2
B. 3/4 mv^2
COM23. Three smiley faces are situated along the x axis as follows: m 1 = 5 kg at 3.0 m, m 2 = 3 kg at 6.0 m and m 3 = 2 kg at 8.0 m. Where is the center of mass situated? A. 3.9 m B. 4.9 m C. 5.5 m D. 4.1 m E. 5.1 m
B. 4.9 m
TAM31. If the sum of the external torques on a system is zero, there is A. a precessional angular velocity. B. a change in the system's angular momentum. C. no change in the system's angular momentum. D. no change in the system's moment of inertia. E. a change in the system's moment of inertia.
C. no change in the system's angular momentum.
E6. To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at: A. the center of mass B. the geometrical center C. the center of gravity D. a point on the boundary E. none of the above
C. the center of gravity
TAM12. A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that vanishes is its: A. angular momentum B. angular acceleration C. total linear momentum D. kinetic energy E. rotational inertia
C. total linear momentum
RRB17. The angular speed of the second hand of a watch is: A. (π/1800) rad/s B. (π/60) m/s C. (π/30) m/s D. (2π) m/s E. (60) m/s
C. (π/30) m/s
RRB26. Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest. A. 3, then 1 and 2 tie B. All are the same C. 1, 2, 3 D. 3, 2, 1 E. 1, 3, 2
C. 1, 2, 3
RRB30. Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a flat disk in the x, y plane 4. a hoop in the x, y planeThe order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:
C. 1, 3, 2, 4
T5. Particle A, with a mass of 4.0 kg, is moving to the left with a speed of 2.0 m/s. Particle B, with a mass of 8.0 kg, is moving to the right with a speed of 30 m/s. What is the velocity of the center of mass of the two particles? A. 1.0 m/s right B. 2.7 m/s left C. 1.3 m/s right D. 1.3 m/s left E. 0 m/s
C. 1.3 m/s right
COM19. For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as: A. the total kinetic energy before the collision B. the difference in the kinetic energies of the objects before the collision C. 1/2Mv2com, where M is the total mass and vcom is the velocity of the center of mass D. the kinetic energy of the more massive body before the collision E. the kinetic energy of the less massive body before the collision
C. 1/2Mv2com, where M is the total mass and vcom is the velocity of the center of mass
T2. A 960 N block is suspended as shown. The beam AB is weightless and is hinged to the wall at A. The tension force of the cable BC has magnitude: A. 1280 N B. 700 N C. 1600 N D. 1400 N E. 1200 N
C. 1600 N
RRB10. The moment of inertia of a set of dumbbells, considered as two mass points m separated by a distance 2 L about the axis AA, is A. mL^2 B. 1/4 mL^2 C. 2mL^2 D. 1/2 mL^2 E. 4mL^2
C. 2mL^2
RRB2. Two points, A and B, are on a disk that rotates about an axis. Point A is three times as far from the axis as point B. If the speed of point B is v, then what is the speed of point A? A. 9v B. v/3 C. 3v D. v E. v/9
C. 3v
T9. A flywheel is accelerated from rest to a rotational speed of 12 rev/s in 6.0 s. The magnitude of the average angular acceleration in rad/s2 during this process is: A. 2 B. 4 C. 4π D. 72 E. 1/π
C. 4π
T6. An ice skater with rotational inertia Io is spinning with angular speed ωo. She pulls her arms in thereby increasing her angular speed to 4ωo. Her rotational inertia is then A. Io/2 B. Io C. Io/4 D. 2 Io E. 4 Io
C. Io/4
An object of mass M 1 is moving with a speed v on a straight, level, frictionless track when it collides with another mass M 2 that is at rest on the track. After the collision, M 1 and M 2 stick together and move with a speed of A. M1v/M2 B. v C. M1v/(M1 + M2) D. M1v E. (M1 + M2)v/M1
C. M 1 v/( M 1 + M 2)
RRB42. A small disk of radius R 1 is fastened coaxially to a larger disk of radius R 2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead veiw below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force ¢ as shown. The tension in the string pulling the block is: A. R1F/R2 B. mR1R2F/(I - mR2^2) C. mR1R2F/(I + mR2^2) D. mR1R2F/(I - mR1R 2) E. mR1R2F/(I + mR1R 2)
C. mR1R2F/(I + mR2^2)
TAM18. When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum: A. must increase B. must decrease C. must remain the same D. may increase or decrease depending on her initial angular velocity E. tilts away from the vertical
C. must remain the same
Q2. A grasshopper has a collision with the windshield of a speeding bus. The largest change in momentum is for the A. the grasshopper B. the bus C. the change is the same for both
C. same (same force, impulse, and momentum)
COM26. The condition necessary for the Conservation of Linear Momentum in a given system is that A. energy is conserved. B. one body is at rest. C. the net external force is zero. D. internal forces equal external forces. E. None of these is correct.
C. the net external force is zero
Q4: A hoop, a solid disk and a solid sphere, all with the same mass and radius, are released at the same time and roll down an incline. Which reaches the bottom first? A. the hoop B. the disk C. the sphere D. all reach the bottom together
C. the sphere The one with the smallest I has the largest acceleration.
E4. For a body to be equilibrium under the combined action of several forces: A. all the forces must be applied at the same point B. all of the forces are composed of pairs of equal and opposite forces C. the sum of the components of all the forces in any direction must equal zero D. any two of these forces must be balanced by a third force E. the lines of action of all the forces must pass through the center of gravity of the body
C. the sum of the components of all the forces in any direction must equal zero
RRB16. If a wheel turns with constant angular speed then: A. each point on its rim moves with constant velocity B. each point on its rim moves with constant acceleration C. the wheel turns through equal angles in equal times D. the angle through which the wheel turns in each second increases as time goes on E. the angle through which the wheel turns in each second decreases as time goes on
C. the wheel turns through equal angles in equal times
RRB6. Power can be expressed as the product of A. force and displacement. B. force and acceleration. C. torque and angular velocity. D. torque and angular displacement. E. torque and angular acceleration.
C. torque and angular velocity.
COM7. The center of mass of a system of particles obeys an equation similar to Newton's second law ¢ = m v com, where: A. ¢ is the total internal force and m is the total mass of the system B. ¢ is the total internal force and m is the mass acting on the system C. ¢ is the total external force and m is the total mass of the system D. ¢ is the force of gravity and m is the mass of Earth E. ¢ is the force of gravity and m is the total mass of the system
C. ¢ is the total external force and m is the total mass of the system
TAM20. A wheel,with rotational inertia I, mounted on a vertical shaft with negligible ratational inertia, is rotating with angular speed ω 0. A nonrotation wheel with rotational inertia 2 I is suddenly dropped onto the same shaft as shown.. The resultant combination of the two wheels and shaft will rotate at: A. ω 0 /2 B. 2ω 0 C. ω 0 /3 D. 3ω 0 E. ω 0 /4
C. ω 0 /3
COM37. In an elastic collision of two objects, A. momentum is conserved, and the kinetic energy after the collision is less than its value before the collision. B. momentum is not conserved. C. momentum is not conserved, and the kinetic energy of the system after the collision differs from the kinetic energy of the system before the collision. D. momentum is conserved, and the kinetic energy after the collision is the same as the kinetic energy before the collision. E. the kinetic energy of the system after the collision depends on the masses of the objects.
D. momentum is conserved, and the kinetic energy after the collision is the same as the kinetic energy before the collision.
If you take the derivative of the kinetic energy of a particle with respect to its velocity, you get A. potential energy. B. acceleration. C. mass. D. momentum. E. force.
D. momentum.
TAM34. A yo-yo, arranged as shown, rests on a table with friction. When a force ¢ is applied to the string as shown, the yo-yo: A. moves to the left and rotates counterclockwise B. moves to the right and rotates counterclockwise C. moves to the left and rotates clockwise D. moves to the right and rotates clockwise E. moves to the right and does not rotate
D. moves to the right and rotates clockwise
RRB29. The rotational inertia of a wheel about its axle does not depend upon its: A. diameter B. mass C. distribution of mass D. speed of rotation E. material composition
D. speed of rotation
Q3: The angular momentum of a system is conserved only if: A. the sum of the external torques equals the sum of the internal torques B. the moment of inertia of the system is constant C. the sum of the internal torques is zero D. the sum of the external torques is zero
D. the sum of the external torques is zero
E5. For a body to be in equilibrium under the combined action of several forces: A. all the forces must be applied at the same point B. all of the forces are composed of pairs of equal and opposite forces C. any two of these forces must be balanced by a third force D. the sum of the torques about any point must equal zero E. the lines of action of all the forces must pass through the center of gravity of the body
D. the sum of the torques about any point must equal zero
Q3. If the total momentum of a system is changing.: A. the particles in the system must be exerting forces on each other B. the system must be under the influence of gravity C. the center of mass must have a constant velocity D. there must be a net external force acting on the system
D. there must be a net external force acting on the system
Q1. The linear momentum of a body is defined as the product of the mass and the A. distance the body moves B. time it takes to move C. acceleration of the body D. velocity of the body
D. velocity of the body
Q4. The linear momentum of a body is defined as the product of the mass and the A. distance the body moves B. time it takes to move C. acceleration of the body D. velocity of the body
D. velocity of the body
COM15. A ball hits a wall and rebounds with the same speed, as diagrammed below. The changes in the components of the momentum of the ball are: A. Δpx > 0, Δpy > 0 B. Δpx < 0, Δpy > 0 C. Δpx > 0, Δpy < 0 D. Δpx = 0, Δpy > 0 E. Δpx = 0, Δpy < 0
D. Δpx = 0, Δpy > 0
RRB22. The fan shown has been turned off and is slowing as it rotates clockwise. The direction of the acceleration of the acceleration point X on the fan tip could be: A. ª B. © C. ↓ D. ← E. →
D. ←
Q3. The angular momentum for a particle in four situations is listed. In which situation is the net torque zero? A.L = 3t + 4 B.L = -6t2 C.L = 4/t D.L = 2 E.none of these
D.L = 2 torque = angular momentum (L) x time (t)
TAM13. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momenta after a given time t, least to greatest. A. hoop, sphere, disk B. hoop, disk, sphere C. hoop, disk, sphere D. disk, hoop, sphere E. all tie
E. all tie
COM1. The center of mass of a uniform disk of radius R is located: A. on the rim B. a distance R/2 from the center C. a distance R/3 from the center D. a distance 2R/3 from the center E. at the center
E. at the center
E25. An upright refrigerator tips over if its A. center of mass is below its middle. B. center of mass is at its middle. C. height is greater than its width. D. center of mass is above its middle. E. center of mass projects onto the floor at a point outside the outline of its base.
E. center of mass projects onto the floor at a point outside the outline of its base.
E11. A picture can be hung on a wall in three different ways, as shown. The tension in the string is: A. least in I B. greatest in I C. greatest in II D. least in III E. greatest in III
E. greatest in III
TAM16. A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms: A. his angular velocity increases B. his angular velocity remains the same C. his rotational inertia decreases D. his rotational kinetic energy increases E. his angular momentum remains the same
E. his angular momentum remains the same
COM36. In a real collision, A. kinetic energy is conserved. B. both momentum and kinetic energy are conserved. C. neither momentum nor kinetic energy is conserved. D. the extent to which momentum and kinetic energy are conserved depends on the coefficient of restitution. E. linear momentum is conserved in the absence of external forces.
E. linear momentum is conserved in the absence of external forces.
TAM21. A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then: A. mv/I B. v/R C. mRv/I D. 2mRv/I E. mRv/(mR^2 + I)
E. mRv/(mR^2 + I)
E3. For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about: A. the center of mass B. the center of gravity C. the geometrical center D. the point of application of the force E. the same point
E. the same point
TAM1. A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by →. Point P is painted on the rim of the wheel. The instantaneous velocity of point P is: A. → B. ← C. ↑ D. « E. zero
E. zero
RRB37. A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force ¢ 1 is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force ¢ 2 (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate: A. ¢2 > ¢1 for some orientations of ¢2 and ¢2 < ¢1 for others B. ¢2 > ¢1 for some orientations of ¢2 and ¢2 = ¢1 for others C. ¢2 = ¢1 for all orientations of ¢2 D. ¢2 < ¢1 for all orientations of ¢2 E. ¢2 > ¢1 for all orientations of ¢2
E. ¢2 > ¢1 for all orientations of ¢2
RRB35. The meter stick shown below rotates about an axis through the point marked •, 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest. A. ¢2 and ¢5 tie, then ¢4, ¢1, ¢3 B. ¢1, ¢2, ¢3, ¢4, ¢5 C. ¢1 and ¢2 tie, then ¢3, ¢4, ¢5 D. ¢2, ¢5, ¢1, and ¢3 tie, then ¢4 E. ¢2 and ¢5 tie, then ¢4, then ¢1 and ¢3 tie
E. ¢2 and ¢5 tie, then ¢4, then ¢1 and ¢3 tie
