AP Physics Help

1. Above is a graph of the distance vs. time for car moving along a road. According the graph, at which of the following times would the automobile have been accelerating positively?

(C) 5, 29, & 57 min.

18. A disk sliding on a horizontal surface that has negligible friction collides with a rod that is free to move and rotate on the surface, as shown in the top view to the right. Which of the following quantities must be the same for the disk-rod system before and after the collision? Select two answers.

A. Linear Momentum B. Angular Momentum

4. A pendulum bob of mass m on a cord of length L is pulled sideways until the cord makes an angle θ with the vertical as shown in the figure to the right. The change in potential energy of the bob during the displacement is:

A. mgL (1-cos θ)

9. A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is

B. 2FR

14. The linear acceleration of the person's hand during the time interval Δt is

B. 2g

Same From 1

B. Determine the inverse of the slope of the best-fit line. Need to find the rotation inertia, so the equation Inertia = sum of torque/ change in acceleration

A wooden board of unknown mass is placed on a fulcrum and remains in static equilibrium, as shown in Figure 1. One end of a string is attached to an object of unknown mass, as shown in Figure 2, and can be hung from the board. A student must hang three objects from the wooden board so that the board does not rotate. The student must then mathematically verify whether or not the system remains in static equilibrium. Which two of the following measurements should the student collect in order to make the verification? Justify your selections. Select two answers.

B. The mass of each object, because each object exerts an external force on the board. D. The horizontal distance each hanging object is from the tip of the fulcrum, because this distance is perpendicular to the direction of the force that a hanging object applies to the board. For both: Torque exerted on the board from each hanging object must be determined.

5. A pendulum is pulled to one side and released. It swings freely to the opposite side and stops. Which of the following might best represent graphs of kinetic energy (Ek), potential energy (Ep) and total mechanical energy (ET)?

C.

7. The graph shows the force on an object of mass M as a function of time. For the time interval 0 to 4 s, the total change in the momentum of the object is

C. 0 kg m/s

8. An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?

D. 1/16 W

13. the net force on the cylinder during the time interval Δt is

D. mgR - Τ

A student is asked to design an experiment to determine the change in angular momentum of a disk that rotates about its center and the product of the average torque applied to the disk and the time interval in which the torque is exerted. A net force is applied tangentially to the surface of the disk. The rotational inertia of the disk about its center is I=12MR2. Which two of the following quantities should the student measure to determine the change in angular momentum of the disk after 10s? Select two answers.

A. The magnitude of the net force exerted on the disk B. The distance between the center of the disk and where the net force is applied to the disk This experiment is an application of the angular impulse-momentum theorem.

Consider the situation in which three identical spheres of clay are launched simultaneously, one along each possible path. All three spheres of clay are launched with the same initial linear speed and collide with the rod at the same time. The time of collision with the rod for each sphere is time t0. Which of the following predictions is correct about the motion of the system containing the rod and all three spheres of clay immediately after the collision?

A. The system will rotate in the clockwise direction with a constant angular speed. The sphere traveling along path Y has a greater magnitude of angular momentum about the pivot than the sphere traveling along path X, while the sphere traveling along path Z has zero angular momentum. Thus, the total angular momentum is in the direction determined by the sphere traveling along path Y, which is clockwise. After the collision, there is no net torque exerted on the rod, so the angular speed is constant.

A disk is fixed to a horizontal axle that extends between two supports, as shown in the figure. Frictional forces between the axle and the supports is not negligible. At time ts, the disk rotates about the center axle with an initial angular speed wd. A student measures the angular displacement Δθ0 of a point on the edge of the disk from time ts until the disk no longer rotates. The angular acceleration of the disk is determined to be αd, and this value remains constant. Based on the data, if possible, how could the student predict the angular displacement of a point on the edge of the disk from time ts until the disk no longer rotates if the initial angular speed is increased to 2ωd ? Justify your selection.

A. Use the equation ω2=ω20+2α(θ−θ0), because the disk comes to rest, ω0=2ωd, and α=αd. Solve for θ−θ0 Although a term for time has been measured by the student, it is not necessary to solve for the angular displacement of a point on the edge of the disk. This mathematical procedure can be used to make the determination, because the only term that changes is ω0=2ωd.

In an experiment, one end of a light string is attached and wrapped around a pulley of diameter 0.5 m. The other end of the string is connected to a block of mass 0.5 kg. The block is released from rest, and the pulley begins to spin in the counterclockwise direction, as shown in Figure 1. Students collect the necessary data to create the graph of the magnitude of the angular momentum of the pulley as a function of time shown in Figure 2. The students state that the graph shows that the net torque exerted on the pulley is constant. Do the data from the graph support the students' statement? Justify your selection.

A. Yes, because the slope of the best-fit line is constant. The slope of a graph of an object's or point's angular momentum as a function of time represents the net torque exerted on the object or point under consideration. The slope of the best-fit line shown in the graph is constant. That means that the student's data from the graph support the student's statement.

2. Three forces act on an object. If the object is moving to the right in translational equilibrium, which of the following must be true? Select two answers.

A: The vector sum of the three forces must equal zero. D: The object must be moving at a constant speed.

An object of mass M hangs from a string that is looped around a pulley of negligible friction, as shown. The pulley has a mass 0.5M. The object is released from rest and it falls to the floor at time t1. Which of the following pairs of graphs best represents the angular speed as a function of time for the pulley and the vertical speed as a function of time for the falling object for a short time after it is released from rest?

Angular Speed: Constant speed then straight line forward Vertical Speed: Constant but straight line going down The only force exerted on the pulley that produces a torque on the pulley is the force of tension from the string that is connected to the object. The force of tension in the string remains constant as the object falls to the ground. Therefore, the angular speed of the pulley should change by a constant amount for a particular time interval. Therefore, the angular acceleration of the pulley should remain constant (the slope of the curve on the angular speed versus time graph) until the object reaches the ground and the string is no longer exerting a torque on the pulley. When this occurs at time t1, the pulley will continue to rotate with a constant angular speed, because no net torque is exerted on the pulley to change its angular speed. The falling object travels in the vertical direction with a constant acceleration that is the result of the net force that is exerted on the object. Therefore, the vertical speed of the object should change by a constant amount for a particular time interval. As a result, the acceleration of the object should remain constant (the slope of the curve on the vertical speed versus time graph) until the object reaches the ground. When this occurs at time t1, the object should then remain at rest.

A rod may freely rotate about an axis that is perpendicular to the rod and is along the plane of the page. The rod is divided into four sections of equal length of 0.2m each, and four forces are exerted on the rod, as shown in the figure. Frictional forces are considered to be negligible. Which of the following correctly describes an additional torque that must be applied in order to keep the rod from rotating?

B. 18N⋅m counterclockwise The combined torque from the four forces can be determined by using vector addition for each individual torque exerted on the rod. Assume positive torques cause the rod to rotate in the clockwise direction. The combined torque exerted on the rod from the three individual forces is positive. That means that this combined torque would cause the rod to rotate clockwise. Since the rod should not rotate, the angular acceleration of the rod will be zero. By Newton's second law of motion in the context of rotational motion, the net torque exerted on the rod must be zero if the rod does not rotate. Therefore, the combined torque exerted on the rod from the three individual forces and the torque exerted on the rod from the additional force must have a vector sum that is equal to zero. Therefore, the torque exerted on the rod from the additional force must be equal to 18N⋅m1 and opposite in direction of the combined torque exerted on the rod from the three individual forces. Therefore, this torque must exerted so that the rod would rotate counterclockwise.

In an experiment, a torque of a known magnitude is exerted along the edge of a rotating disk. The disk rotates about its center. All frictional forces are considered to be negligible. Which of the following quantities should a student collect in order to determine the change in angular momentum of the disk for a specific time interval? Justify your selection.

B. The amount of time the torque is applied to the disk, because the time interval is related to the angular impulse of the disk. This experiment is an application of the angular impulse-momentum theorem. ΔL=τΔt The torque of known magnitude exerted on the disk is also considered to be the net torque exerted on the disk. Therefore, only the time interval for which the net torque is applied to the disk should be measured or determined.

A disk that can freely spin about a central axis is initially at rest until a net force is applied to the disk. The net force is exerted tangentially on the edge of the disk, which has radius 0.5m, mass 0.25kg, and rotational inertia 0.0625kg⋅m2. The magnitude of the force as a function of time is shown in the graph. Which two of the following statements are correct about the disk? Select two answers.

B. The disk's angular acceleration at 10s is 40rad/s2. D. The final angular momentum of the disk at 10s is 12.5kg⋅m2/s. Take the L too lazy to explain.

The graph shown represents the net torque that a wrench exerts on a bolt as a function of time as the wrench turns the bolt around its central axis of rotation. What is the change in angular momentum of the bolt after 1000 ms?

C. 3.0 kg⋅m2/s The area bound by the curve and the horizontal axis from 0 ms to 1000 ms for the graph of the net torque exerted on the bolt that rotates as a function of time represents the angular impulse exerted on the bolt. A=1/2bh ΔL=12(1.0 s)(6 N⋅m) ΔL=3.0 kg⋅m2/s

3. Three blocks of masses 3m, 2m, and m are connected to strings A, B, and C as shown above. The blocks are pulled along a rough surface by a force of magnitude F exerted by string C. The coefficient of friction between each block and the surface is the same. Which string must be the strongest in order not to break?

C. C

In an experiment, a solid, uniform disk of mass 0.2kg and radius 0.5m is suspended vertically and can rotate about its center axle such that frictional forces are considered to be negligible. A string is wrapped around the pulley with one end connected to a block of mass 0.1kg that hangs from the string at rest, as shown in Figure 1. The block is released from rest and falls to the ground as the pulley rotates. A student collects the necessary data to construct a graph of the net force exerted on the edge of the pulley as a function of time, as shown in Figure 2. How can the student use the graph in Figure 2 to determine the change in angular momentum of the disk from 0 s to 4 s?

C. Determine the area bound by the best fit curve and the horizontal axis from 0 s0 s to 4 s4 s and multiply the result by the radius of the disk. When provided with a graph of the net force exerted on an object as a function of time, the area bound by the curve and the horizontal axis for a specific interval of time represents the impulse of the object. In this case, when the impulse is multiplied by the radius of the disk, the angular impulse exerted on the disk is determined. The angular impulse of the disk represents the change in angular momentum of the disk.

10. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?

C. III

Disk Y of rotational inertia IY about its center is held at rest above disk X of rotational inertia IX about its center. Disk X rotates about its center with an angular velocity +ω1. Disk Y is slowly lowered onto disk X until both disks are in contact and travel together with a common angular velocity. A graph of disk X's angular acceleration α as a function of time is shown. Which of the following equations can a student use to verify that angular momentum is conserved in the situation? Justify your selection.

C. IXω1=(IX+IY)(ω1−α5t1), because the final velocity of the two-disk system is equal to the initial velocity of disk XX minus the magnitude of the area bound by the curve and the horizontal axis from 32t1 to 52t1. The area bound by the curve and the horizontal axis for a particular time interval for a graph of an object's or point's angular acceleration as a function of time is equal to the change in the angular velocity of the object. The final angular velocity of the two-disk system must then be determined. When both disks rotate together with a common angular velocity after disk Y is lowered onto disk X, their angular momenta add such that the rotational inertia for each disk is added together, as shown. A=bh Δω=Δtα Δω=−α5t1 Δω=ωf−ω0 ωf=Δω+ω0 ωf=ω1−α5t1

A sphere of clay travels toward the rod along path Z. A student must predict what will happen to the linear momentum and the angular momentum of the rod-sphere system as a result of the collision. Which of the following correctly predicts the change, if any, of these quantities?

C. Linear Momentum: Decreases Angular Momentum: No Change Immediately before the collision, the sphere of clay that travels along path Z has a linear momentum that is along the same direction as its velocity vector. Therefore, the linear momentum of the rod-sphere system is nonzero. However, immediately after the collision, the sphere of clay collides with and sticks to the rod. However, the rod remains fixed in place. Therefore, the sphere-rod system will be at rest immediately after the collision. The linear momentum of the sphere-rod system is zero immediately after the collision. When the sphere of clay that travels along path Z collides with and sticks to the rod, the force exerted on the rod from the clay is exerted along a line that passes through the potential axis of rotation for the sphere-rod system. A net torque is not exerted on the rod during the collision, because an external force is not applied to the sphere-rod system. Since a net torque is not exerted on the sphere-rod system, the angular momentum of the system does not change from immediately before the collision to immediately after the collision.

An isolated spherical star of radius R0 rotates about an axis that passes through its center with an angular velocity of ω0. Gravitational forces within the star cause the star's radius to collapse and decrease to a value r0<R0, but the mass of the star remains constant. A graph of the star's angular velocity as a function of time as it collapses is shown. Which of the following predictions is correct about the angular momentum L⃗ of the star immediately after the collapse?

C. L→ will be the same as before the collapse. A net external torque is not exerted on the star because it is considered to be an isolated system. Therefore, the angular momentum of the star will be the same before, during, and after the collapse.

6. Two objects, P and Q, have the same momentum. Q can have more kinetic energy than P if it has:

C. More speed than P

16. An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?

C. Remains Constant

A student conducts an experiment to test the relationship between the net torque exerted on an object and the change in angular momentum of the object. A variable net torque is exerted on the object to make it rotate about its internal axis. Data from the experiment are used to construct a graph of the net torque exerted on the object as a function of time, as shown in Figure 1. A graph is also created of the angular momentum of the object as a function of time, as shown in Figure 2. Which of the following statements about the change in the object's angular momentum for a given time interval is correct? Justify your selection.

C. The change in the object's angular momentum for a given time interval does not remain the same throughout the experiment. This is because the slope of the best-fit line in Figure 1 is a nonzero constant. The slope of the graph shown in Figure 1 represents how much the net torque on the object increases per unit of time. The slope of the graph is constant, which means that the net torque exerted on the object increases by the same amount for a particular unit of time. According to the angular analog of the impulse-momentum theorem, the net torque is directly proportional to the change in the angular momentum of the object as expressed by the equation ΔL=ΣτΔt. Therefore, the change in the angular momentum for a particular time interval will be different as the net torque increases over time.

A student conducts an experiment in which a disk may freely rotate around its center in the absence of frictional forces. The student collects the necessary data to construct a graph of the rod's angular momentum as a function of time, as shown. The student makes the following claim. "The graph shows that the magnitude of the angular acceleration of the disk decreases as time increases." Which of the following statements is correct about the student's evaluation of the data from the graph? Justify your selection.

C. The student is incorrect, because the graph shows that the net torque exerted on the disk is constant as time increases. The slope of the best-fit curve of a graph of an object's or point's angular momentum as a function of time represents the net torque exerted on the object or point under consideration. The slope of the best-fit curve in the graph created by the student is constant. Therefore, the net torque exerted on the rod must also be constant. The net torque is directly proportional to the angular acceleration of the disk. Therefore, the angular acceleration of the disk remains constant as time increases.

12. A turntable that is initially at rest is set in motion with a constant angular acceleration α. What is the angular velocity of the turntable after it has made one complete revolution?

C. √4πα

17. The rigid body shown in the diagram to the right consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed ω. If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?

D. 1/8

15. A bowling ball of mass M and radius R, whose moment of inertia about its center is (2/5)MR2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is

D. 7v^2/10g

A rod is at rest on a horizontal surface. One end of the rod is connected to a pivot that allows the rod to rotate around the pivot after a net external force is exerted on the rod. A lump of clay is launched horizontally toward the free end of the rod, as shown in Figure 1. The lump of clay collides with the rod but does not stick to the rod. The lump of clay comes to rest as the rod rotates around the pivot, as shown in Figure 2. Which of the following linear collisions is analogous to the rotational collision that is described?

D. A block traveling in the positive direction collides with a second block that is at rest. After the collision, the first block comes to rest and the second block travels at a nonzero speed in the direction that the first object initially traveled. The collision under consideration is an elastic collision. In the rotational case, the lump of clay is initially traveling toward the rod that is at rest. The lump of clay collides with the rod, and the lump of clay comes to rest. Immediately after the collision, the rod travels with a nonzero angular velocity that is in the direction of the lump of clay's angular velocity immediately before the collision.

A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects the rotational motion of the door. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero. Which of the following lists what measuring devices the students need and the measurements they should take to collect the necessary data to test the relationship between a torque exerted on the door and the change in angular velocity of that object about the hinges of the door? Justify your selection.

D. A stopwatch to measure the time interval during which the force is applied, a force probe to measure the applied force on the door, a protractor to measure the angular displacement of the door, and a meterstick to measure the radial distance from the door's hinges to the location where the force is applied. To mathematically describe the torque that is exerted on an object, the magnitude of the force exerted on the object (measured with a force probe and assumed to be of constant magnitude) and the radial distance from the axis of rotation that the force is applied (measured with a meterstick) must be known. To mathematically describe the change in angular velocity of an object from rest, its change in angular position (measured with a protractor) in an interval of time (measured with a stopwatch) must also be known.

A net torque is applied to the edge of a spinning object as it rotates about its internal axis. The table shows the net torque exerted on the object at different instants in time. How can a student use the data table to determine the change in angular momentum of the object from 0s to 6s? Justify your selection.

D. Create a graph of net torque as a function of time and graph four points of data by using the table. Determine the area bound by the curve and the horizontal axis from 0s to 6s, because the shape of the curve on the graph will be a right triangle and the area can be directly determined. The area bound by the curve and the horizontal axis for a particular time interval for the graph of the net torque exerted on a point that rotates as a function of time represents the angular impulse exerted on the point. The angular impulse is equal to the change in angular momentum of the object under consideration.

Which of the following graphs qualitatively represents the angular velocity ω of the point on the disk as a function of time t between 0s to 2s?

D. Graph starts in the 4th quadrant on y-axis then cross up to 1st quadrant. The initial angular velocity of the point on the disk is 3rad/s clockwise. This means that the initial angular velocity vector is in the negative direction. The angular acceleration of the point on the disk is +6rad/s2. Therefore, the angular acceleration vector of the point on the disk is in the counterclockwise direction. Therefore, initially, the disk rotates clockwise. However, the angular acceleration of the disk will cause the disk to slow down until it comes to rest. Then the disk will rotate counterclockwise with an increasing speed, because the angular acceleration vector will always be in the same direction as the angular velocity vector.

An ice skater rotates in a circle about an internal axis of rotation. Figure 1 shows the skater with her arms extended fully outward. Figure 2 shows the skater with her arms partially inward to her body. Figure 3 shows the skater with her arms completely inward and in contact with her body. Which of the following claims is correct about the angular momentum of the skater?

D. The angular momentum of the skater is the same in all figures. A net torque is not exerted on the skater as the skater brings her arms in closer to her body. Although the skater's angular speed increases as the skater brings her arms in close to her body, the skater's rotational inertia decreases. Therefore, the angular momentum of the skater is conserved and is the same in all figures.

11. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?

D. mω2r + mg