College Physics I
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the angular speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4
A) 1:1
Which one of the following statements concerning streamline flow is true? A) At any given point in the fluid, the velocity is constant in time. B) Streamline flow occurs when there are sharp obstacles in the path of a fast-moving fluid. C) Streamline flow is described by Pascal's principle. D) Streamline flow is described by Archimedes' principle. E) The velocity vectors are the same for all particles in the fluid.
A) At any given point in the fluid, the velocity is constant in time.
A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. Which one of the following statements is true concerning the angular momentum of this hoop? A) It points into the paper. B) It points out of the paper. C) It points to the left. D) It points to the right. E) It varies from point to point on the hoop.
A) It points into the paper.
What are the SI units of the shear modulus? A) N/m^2 B) N/m C) N ⋅ m D) N/m^3 E) N ⋅ m^2
A) N/m^2
Complete the following sentence: The operation of a hydraulic jack is an application of A) Pascal's principle. B) Bernoulli's principle. C) Archimedes' principle. D) irrotational flow. E) the continuity equation
A) Pascal's principle.
Which law, principle, or equation can be used to determine the volume flow rate of a liquid that is forced through a hypodermic needle? A) Poiseuille's law B) Pascal's principle C) Bernoulli's equation D) Archimedes' principle E) the equation of continuity
A) Poiseuille's law
Two uniform solid spheres, A and B have the same mass. The radius of sphere B is twice that of sphere A. The axis of rotation passes through each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true? A) The moment of inertia of A is one-fourth that of B. B) The moment of inertia of A is one-half that of B. C) The moment of inertia of A is 5/4 that of B. D) The moment of inertia of A is 5/2 that of B. E) The two spheres have equal moments of inertia.
A) The moment of inertia of A is one-fourth that of B.
A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane. Which one of the following statements is necessarily true? A) The solid sphere will reach the bottom first. B) The hollow sphere will reach the bottom first. C) Both spheres will reach the bottom at the same time. D) The solid sphere will reach the bottom with the greater kinetic energy. E) The hollow sphere will reach the bottom with the greater kinetic energy.
A) The solid sphere will reach the bottom first.
Which one of the following terms is used to describe a system in which the degree of damping is just enough to stop the system from oscillating? A) critically damped B) underdamped C) slightly damped D) overdamped E) resonance
A) critically damped
A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced by another cable of the same material having the same length and twice the diameter. If the same crate is supported by the thicker cable, by how much will the cable stretch? A) d/4 B) d/2 C) d D) 2d E) 4d
A) d/4
A top is spinning counterclockwise as shown in the figure. It is also moving to the right with a linear speed v. What is the direction of the angular velocity? A) upward B) downward C) left D) right E) into the paper
A) upward
Which one of the following expressions gives the displacement of the block as a function of time? Let x be in cm and t in seconds. A) x = 15 cos(14πt) B) x = 15 sin(14πt) C) x = 7 cos(15πt) D) x = 14 sin(15πt) E) x = 44 cos(14πt)
A) x = 15 cos(14πt)
Complete the following statement: The angular measure 1.0 radian is equal to A) 0.0175°. B) 57.3°. C) 1.57°. D) 3.14°. E) 6.28°.
B) 57.3°.
A curtain hangs straight down in front of an open window. A sudden gust of wind blows past the window; and the curtain is pulled out of the window. Which law, principle, or equation can be used to explain this movement of the curtain? A) Poiseuille's law B) Bernoulli's equation C) the equation of continuity D) Archimedes' principle E) Pascal's principle
B) Bernoulli's equation
Which one of the following statements concerning Hooke's law is false? A) Hooke's law relates stress and strain. B) Hooke's law is valid only for springs. C) Hooke's law can be verified experimentally. D) Hooke's law can be applied to a wide range of materials. E) Hooke's law is valid only within the elastic limit of a given material.
B) Hooke's law is valid only for springs.
Which one of the following statements concerning the moment of inertia I is false? A) I may be expressed in units of kg ⋅ m2. B) I depends on the angular acceleration of the object as it rotates. C) I depends on the location of the rotation axis relative to the particles that make up the object. D) I depends on the orientation of the rotation axis relative to the particles that make up the object. E) Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to I.
B) I depends on the angular acceleration of the object as it rotates.
A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller? A) The star's angular velocity decreases. B) The star's angular momentum remains constant. C) The star's angular momentum increases. D) The star's angular velocity remains constant. E) Both the star's angular momentum and its angular velocity remain constant.
B) The star's angular momentum remains constant.
A satellite follows a circular path with constant speed around a planet. Which one of the following quantities is constant and non-zero for this satellite? A) linear velocity B) angular velocity C) centripetal acceleration D) angular acceleration E) total acceleration
B) angular velocity
A cable stretches by an amount d when it supports a crate of mass M. The cable is then cut into three equal pieces. If the same crate is supported by any one of these pieces, by how much will the cable stretch? A) d B) d/3 C) d/6 D) 3d E) 9d
B) d/3
Complete the following statement: In order to increase the frequency of the motion, one would have to A) reduce the spring constant. B) decrease the mass of the block on the end of the spring. C) increase the length of the spring. D) reduce the distance that the spring is initially stretched. E) increase the distance that the spring is initially stretched.
B) decrease the mass of the block on the end of the spring.
A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M easily slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time from the top of their inclined planes, A) the cylinder will reach the bottom first. B) the block will reach the bottom first. C) the block will reach the bottom with the greater kinetic energy. D) the cylinder will reach the bottom with the greater kinetic energy. E) both the block and the cylinder will reach the bottom at the same time.
B) the block will reach the bottom first.
Complete the following statement: In order to calculate the "stress" on the box, in addition to the information given, one must also know A) the mass of the box. B) the bulk modulus of the material from which the box is made. C) the shear modulus of the material from which the box is made. D) the Young's modulus of the material from which the box is made. E) the bulk modulus of the liquid.
B) the bulk modulus of the material from which the box is made.
Consider the following three objects, each of the same mass and radius: (1) a solid sphere (2) a solid disk (3) a hoop All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline? A) 3, 1, 2 B) 2, 3, 1 C) 1, 2, 3 D) 3, 2, 1 E) All three reach the bottom at the same time.
C) 1, 2, 3
A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2. Determine the ratio of her final kinetic energy to her initial kinetic energy. A) 0.5 B) 1 C) 2 D) 4 E) 16
C) 2
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the centripetal acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4
C) 2:1
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the tangential acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4
C) 2:1
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the tangential speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4
C) 2:1
Which one of the following statements concerning a completely enclosed fluid is true? A) Any change in the applied pressure of the fluid produces a change in pressure that depends on direction. B) The pressure at all points within the fluid is independent of any pressure applied to it. C) Any change in applied pressure produces an equal change in pressure at all points within the fluid. D) An increase in pressure in one part of the fluid results in an equal decrease in pressure in another part. E) The pressure in the fluid is the same at all points within the fluid.
C) Any change in applied pressure produces an equal change in pressure at all points within the fluid.
A circular hula hoop rolls upright without slipping on a flat horizontal surface. Which one of the following statements is necessarily true? A) All points on the rim of the hoop have the same speed. B) All points on the rim of the hoop have the same velocity. C) Every point on the rim of the wheel has a different velocity. D) All points on the rim of the hoop have acceleration vectors that are tangent to the hoop. E) All points on the rim of the hoop have acceleration vectors that point toward the center of the hoop.
C) Every point on the rim of the wheel has a different velocity.
What happens when a spinning ice skater draws in her outstretched arms? A) Her angular momentum decreases. B) Her angular momentum increases. C) Her moment of inertia decreases causing her to speed up. D) Her moment of inertia decreases causing her to slow down. E) The torque that she exerts increases her moment of inertia.
C) Her moment of inertia decreases causing her to speed up.
A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 2.0 kg. Its volume is 5.0 m3. The density of air is 1.3 kg/m3. Will the balloon rise, fall, or remain stationary; and why? A) The balloon will fall because its density is greater than that of air. B) The balloon will remain stationary because its density is less than that of air. C) The balloon will rise because the upward buoyant force is greater than its weight. D) The balloon will fall because the upward buoyant force is less than its weight. E) The balloon will fall because the downward buoyant force is greater than the upward buoyant force.
C) The balloon will rise because the upward buoyant force is greater than its weight.
Complete the following statement: In general, the term stress refers to A) a change in volume. B) a change in length. C) a force per unit area. D) a fractional change in length. E) a force per unit length.
C) a force per unit area.
A ball of mass M moves in a circular path on a horizontal, frictionless surface. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase. Complete the following sentence: This occurs because A) the linear momentum of the ball is conserved. B) it is required by Newton's first law of motion. C) the angular momentum of the ball is conserved. D) the angular momentum of the ball must increase. E) the total mechanical energy of the ball must remain constant.
C) the angular momentum of the ball is conserved.
Consider the following four objects: a hoop, a flat disk, a solid sphere, and a hollow sphere. Each of the objects has mass M and radius R. The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk. Which of these objects requires the largest torque to give it the same angular acceleration? A) the solid sphere B) the hollow sphere C) the hoop D) the flat disk E) both the solid and the hollow spheres
C) the hoop
A cable stretches by an amount d as it supports a crate of mass M. The cable is cut in half. What is the mass of the load that can be supported by either half of the cable if the cable stretches by an amount d? A) M/4 B) M/2 C) M D) 2M E) 4M
D) 2M
What is the total mechanical energy of the system at any instant? A) 0.25 J B) 0.49 J C) 0.98 J D) 4.4 J E) 9.8 J
D) 4.4 J
Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true? A) Both points have the same centripetal acceleration. B) Both points have the same tangential acceleration. C) The angular velocity at point A is greater than that of point B. D) Both points have the same instantaneous angular velocity. E) Each second, point A turns through a greater angle than point B
D) Both points have the same instantaneous angular velocity.
The figure shows two fish tanks, each having ends of width 1 foot. Tank A is 3 feet long while tank B is 6 feet long. Both tanks are filled with 1 foot of water. SA = the magnitude of the force of the water on the end of tank A SB = the magnitude of the force of the water on the end of tank B BA = the magnitude of the force of the water on the bottom of tank A BB = the magnitude of the force of the water on the bottom of tank B Using the notation given above, which one of the following sets of equations below is correct for this situation? A) SA = SB and BA = BB B) SA = 2SB and BA = BB C) 2SA = SB and 2BA = BB D) SA = SB and 2BA = BB E) SA = 2SB and BA = 2BB
D) SA = SB and 2BA = BB
A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why? A) The angular speed of the system decreases because the moment of inertia of the system has increased. B) The angular speed of the system increases because the moment of inertia of the system has increased. C) The angular speed of the system decreases because the moment of inertia of the system has decreased. D) The angular speed of the system increases because the moment of inertia of the system has decreased. E) The angular speed of the system remains the same because the net torque on the merry-go-round is zero N ⋅ m.
D) The angular speed of the system increases because the moment of inertia of the system has decreased.
Which one of the following statements concerning the buoyant force on an object submerged in a liquid is true? A) The buoyant force depends on the mass of the object. B) The buoyant force depends on the weight of the object. C) The buoyant force is independent of the density of the liquid. D) The buoyant force depends on the volume of the liquid displaced. E) The buoyant force will increase with depth if the liquid is incompressible.
D) The buoyant force depends on the volume of the liquid displaced.
Which one of the following statements is true concerning an object executing simple harmonic motion? A) The object's velocity is never zero. B) The object's acceleration is never zero. C) The object's velocity and acceleration are simultaneously zero. D) The object's velocity is zero when its acceleration is a maximum. E) The object's maximum acceleration is equal to its maximum velocity.
D) The object's velocity is zero when its acceleration is a maximum.
Complete the following statement: Young's modulus cannot be applied to A) a stretched wire. B) a compressed rod. C) a bending beam. D) a compressed liquid. E) a stretched rubber band
D) a compressed liquid.
A compact disc rotates about its center at constant angular speed. Which one of the following quantities is constant and non-zero for a dust particle near the edge of the disc? A) linear velocity B) torque about the center of the disc C) centripetal acceleration D) angular momentum E) angular acceleration
D) angular momentum
Complete the following statement: Bernoulli's principle is a statement of A) hydrostatic equilibrium. B) thermal equilibrium in fluids. C) mechanical equilibrium in fluids. D) energy conservation in dynamic fluids. E) momentum conservation in dynamic fluids.
D) energy conservation in dynamic fluids.
Complete the following statement: A body is in translational equilibrium A) only if it is at rest. B) only if it is moving with constant velocity. C) only if it is moving with constant acceleration. D) if it is either at rest or moving with constant velocity. E) if it is moving with either constant velocity or constant acceleration.
D) if it is either at rest or moving with constant velocity.
A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of length L. The ball is displaced from its equilibrium position by a small angle θ. What is the magnitude of the restoring force that moves the ball toward its equilibrium position and produces simple harmonic motion? A) kx B) mg C) mg(cos θ) D) mg(sin θ) E) mgL(sin θ)
D) mg(sin θ)
Complete the following sentence: Resonance occurs in harmonic motion when A) the system is overdamped. B) the system is critically damped. C) the energy in the system is a minimum. D) the driving frequency is the same as the natural frequency of the system. E) the energy in the system is proportional to the square of the motion's amplitude.
D) the driving frequency is the same as the natural frequency of the system.
A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy? A) 33 % B) 50 % C) 12 % D) 75 % E) 29 %
E) 29 %
A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced by another cable of the same material having the same length and twice the diameter. What is the mass of the load that can be supported by the thicker cable if it stretches by an amount d? A) M/4 B) M/2 C) M D) 2M E) 4M
E) 4M
A solid sphere of radius R rotates about a diameter with an angular speed ω. The sphere then collapses under the action of internal forces to a final radius R/2. What is the final angular speed of the sphere? A) ω/4 B) ω/2 C) ω D) 2ω E) 4ω
E) 4ω
Which one of the following statements concerning fluid streamlines is true? A) In steady flow, streamlines must remain parallel and equally spaced. B) In turbulent flow, two or more streamlines may cross. C) In turbulent flow, streamlines can begin or end at any point. D) Streamlines are perpendicular to the velocity of the fluid at every point. E) In steady flow, the pattern of streamlines does not change with time.
E) In steady flow, the pattern of streamlines does not change with time.
Which one of the following statements most accurately describes the center of gravity of an object? A) It is the point where gravity acts on the object. B) It is the point where all the mass is concentrated. C) It must be experimentally determined for all objects. D) It is the point on the object where all the weight is concentrated. E) It is the point from which the torque produced by the weight of the object can be calculated.
E) It is the point from which the torque produced by the weight of the object can be calculated.
Which one of the following statements is true concerning the motion of the block? A) Its acceleration is constant. B) The period of its motion depends on its amplitude. C) Its acceleration is greatest when the spring returns to the 5.0 cm position. D) Its velocity is greatest when the mass has reached its maximum displacement. E) Its acceleration is greatest when the mass has reached its maximum displacement.
E) Its acceleration is greatest when the mass has reached its maximum displacement.
A u-shaped tube is connected to a flexible tube that has a membrane-covered funnel on the opposite end as shown in the drawing. Justin finds that no matter which way he orients to membrane, the height of the liquid in the u-shaped tube does not change. Which of the following choices best describes this behavior? A) Archimedes' principle B) Bernoulli's principle C) continuity equation D) irrotational flow E) Pascal's principle
E) Pascal's principle
The two dams are identical with the exception that the water reservoir behind dam A extends twice the horizontal distance behind it as that of dam B. Which one of the following statements regarding these dams is correct? A) The force exerted by the water on dam A is greater than that on dam B. B) The force exerted by the water on dam B is greater than that on dam A. C) Dam A is more likely to collapse than dam B if the water level rises. D) Dam B is more likely to collapse than dam A if the water level rises. E) The horizontal distance of the water behind the two dams does not determine the force on them.
E) The horizontal distance of the water behind the two dams does not determine the force on them.
A rigid body rotates about a fixed axis with a constant angular acceleration. Which one of the following statements is true concerning the tangential acceleration of any point on the body? A) The tangential acceleration is zero m/s2. B) The tangential acceleration depends on the angular velocity. C) The tangential acceleration is equal to the centripetal acceleration. D) The tangential acceleration is constant in both magnitude and direction. E) The tangential acceleration depends on the change in the angular velocity.
E) The tangential acceleration depends on the change in the angular velocity.
Three blocks, labeled A, B, and C, are floating in water as shown in the drawing. Blocks A and B have the same mass and volume. Block C has the same volume, but is submerged to a greater depth than the other two blocks. Which one of the following statements concerning this situation is false?A) The density of block A is less than that of block C. B) The buoyant force acting on block A is equal to that acting on block B. C) The volume of water displaced by block C is greater than that displaced by block B. D) The buoyant force acting on block C is greater than that acting on block B. E) The volume of water displaced by block A is greater than that displaced by block B.
E) The volume of water displaced by block A is greater than that displaced by block B.
Which one of the following statements concerning a wheel undergoing rolling motion is true? A) The angular acceleration of the wheel must be zero m/s2. B) The tangential velocity is the same for all points on the wheel. C) The linear velocity for all points on the rim of the wheel is non-zero. D) The tangential velocity is the same for all points on the rim of the wheel. E) There is no slipping at the point where the wheel touches the surface on which it is rolling.
E) There is no slipping at the point where the wheel touches the surface on which it is rolling.
Which one of the following statements is false concerning the derivation or usage of Bernoulli's equation? A) The fluid must be non-viscous. B) Streamline flow is assumed. C) The fluid must be incompressible. D) The work-energy theorem is used to derive Bernoulli's equation. E) Vertical distances are always measured relative to the lowest point within the fluid.
E) Vertical distances are always measured relative to the lowest point within the fluid.
Complete the following statement: When a net torque is applied to a rigid object, it always produces a A) constant acceleration. B) rotational equilibrium. C) constant angular velocity. D) constant angular momentum. E) change in angular velocity.
E) change in angular velocity.
Changing angular velocity means that an ______________________ is occuring
angular acceleration
Average angular velocity =
angular displacement/elapsed time
Average Angular acceleration
change in angular velocity/elapsed time
SI Unit of Angular Velocity:
radian per second (rad/s)
SI unit for angular acceleration
radian per second squared (rad/s2)
Average angular acceleration α equation
α =(ω-ωo)/(t-to)=∆ω/∆t
Angular velocity ω
ω = (θ-θo)/(t-to)=∆θ/∆t
Instantaneous Angular velocity
ω =lim(∆t->0)ω=lim(∆t->0)∆θ/∆t