Practice Test Rotation

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

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

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

Which of the following statements about the motion of the second hand of a clock is true? A. The tangential acceleration is nonzero. B. The angular acceleration is zero. C. The tangential velocity of the tip is constant. D. The angular velocity is zero. E. The radial acceleration is zero.

B. The angular acceleration is zero.

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 rotational kinetic energy is greater. B. They are equal. C. Its translational kinetic energy is greater. D. The answer depends on the radius. E. The answer depends on the mass.

B. They are equal.

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

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. All are the same B. 1, 3, 2 C. 1, 2, 3 D. 3, then 1 and 2 tie E. 3, 2, 1

C. 1, 2, 3

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 plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is: A. 1, 2, 3, 4 B. 4, 3, 2, 1 C. 1, 3, 2, 4 D. 4, 2, 3, 1 E. 3, 1, 2, 4

C. 1, 3, 2, 4

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 mR2, the moment of inertia about the axis through P is A. mR2 B. 0.4mR2 C. 1.5mR2 D. 2/3 mR2 E. 1/2mR2

C. 1.5mR2

The moment of inertia of a set of dumbbells, considered as two mass points m separated by a distance 2L about the axis AA, is A. 1/2mL2 B. 4mL2 C. 2mL2 D. 1/4mL2 E. mL2

C. 2mL2

When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is: A. ML2/12 B. ML2/6 C. ML2/3 D. 7ML2/12 E. 13ML2/12

C. ML2/3

A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. 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)

Two masses M and m (M > m) are hung over a disc (Idisc = M'R2) and are released so that they accelerate. If T1 is the tension in the cord on the left and T2 is the tension in the cord on the right, then A. T2 = Mg/m B. T2 = Mg C. T2 > T1 D. T1 = T2 E. T2 < T1

C. T2 > T1

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. A. hoop, sphere, disk B. sphere, disk, hoop C. hoop, disk, sphere D. hoop, disk, sphere E. disk, hoop, sphere

C. hoop, disk, sphere

A small disk of radius R1 is fastened coaxially to a larger disk of radius R2. 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 - mR22) C. mR1R2F/(I + mR22) D. mR1R2F/(I - mR1R 2) E. mR1R2F/(I + mR1R 2)

C. mR1R2F/(I + mR22)

A wheel rotates with a constant nonzero angular acceleration. Which of the following quantities remains constant in magnitude? A. tangential velocity B. radial acceleration C. tangential acceleration D. angular velocity E. All of these are correct.

C. tangential acceleration

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

Power can be expressed as the product of A. force and acceleration. B. force and displacement. C. torque and angular velocity. D. torque and angular acceleration. E. torque and angular displacement.

C. torque and angular velocity.

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.

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 acceleration. C. torque and angular displacement. D. force and lever arm. E. torque and angular velocity.

C. torque and angular displacement.

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

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

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. ¢1 and ¢2 tie, then ¢3, ¢4, ¢5 B. ¢1, ¢2, ¢3, ¢4, ¢5 C. ¢2 and ¢5 tie, then ¢4, ¢1, ¢3 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

Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is: A. 3.14 rad/s2 B. 30 rad/s2 C. 30 rev/s2 D. 50 rev/min2 E. 1800 rev/s2

A. 3.14 rad/s2

A cylinder (I = mR2) rolls along a level floor with a speed v. The work required to stop this cylinder is A. 3/4mv2 B. mv2 C. 1/2mv2 D. 1.25mv2 E. 1/4mv2

A. 3/4mv2

The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is: A. 7.0 m/s B. 14π rad/s C. 7π rad/s D. 0.70 m/s E. none of these

A. 7.0 m/s

A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kg ⋅ m2. When the block is released and the cord unwinds, the acceleration of the block is: A. 0.15 g B. 0.56 g C. 0.84 g D. g E. 1.3 g

B. 0.56 g

A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is: A. 2.0 rad/s2 B. -2.0 rad/s2 C. 3.0 rad/s2 D. -3.0 rad/s2 E. 6.0 rad/s2

B. -2.0 rad/s2

A wagon wheel consists of 8 spokes of uniform diameter, each of mass ms and length L cm. The outer ring has a mass mring. 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. (8/3ms+1/4mring)L^2 B. mringL^2 C. (1/3ms+mring)L^2 D. (8/3ms+mring)L^2 E. (8/3ms+1/2mring)L^2

D. (8/3ms+mring)L^2

The angular speed of the minute hand of a watch is: A. (60/π) m/s B. (1800/π) m/s C. (π) m/s D. (π/1800) m/s E. (π/60) m/s

D. (π/1800) m/s

A uniform disk (Io = mR2) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point is A. mR2 B. 2mR2/3 C. 1/2 mR2 D. 1.5mR2 E. 2mR2

D. 1.5mR2

A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is: A. 1/π B. 2 C. 4 D. 4π E. 72

D. 4π

A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is: A. 5.0 rad/s2 B. 3.0 m/s2 C. 5.0 m/s2 D. 6.0 m/s2 E. 12 m/s2

D. 6.0 m/s2

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. ML2/2 C. ML2 D. MR2 E. none of these

D. MR2

Starting from rest at the same time, a coin and a ring roll down an incline without slipping. Which reaches the bottom first? A. They arrive at the bottom simultaneously. B. The winner depends on the relative diameters of the two. C. The ring reaches the bottom first. D. The coin reaches the bottom first. E. The winner depends on the relative masses of the two.

D. The coin reaches the bottom first.

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

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

Two objects, m1 and m2, both of mass m, are place on a horizontal platform which is rotating at a constant angular velocity. m1 = m is located at a distance R from the axis of rotation and the second object of mass m2 = 2m is located at a distance 2R. The angular velocity of mass m1____ to the angular velocity of m2. A. depends how fast it is rotating B. is less than C. unable to tell D. is equal to E. is greater than

D. is equal to

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

The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the acceleratrion point X on the fan tip could be: A. ª B. © C. ↓ D. ← E. →

D. ←

The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, 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. MR2 B. (2/5)MR2 C. (3/5)MR2 D. (5/2)MR2 E. (7/5)MR2

E. (7/5)MR2

Three identical balls, with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is: A. ML2/2 B. ML2 C. 3ML2/2 D. 6ML2 E. 3ML2/4

E. 3ML2/4

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 C. v/3 D. v/9 E. 3v

E. 3v

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 radius. B. They are equal. C. Its rotational kinetic energy is greater. D. The answer depends on the mass. E. Its translational kinetic energy is greater.

E. Its translational kinetic energy is greater.