Physics - Unit 7 Progress Check: MCQ Part A + B

A disk of radius R=0.5cm rests on a flat, horizontal surface such that frictional forces are considered to be negligible. Three forces of unknown magnitude are exerted on the edge of the disk, as shown in the figure. Which of the following lists the essential measuring devices that, when used together, are needed to determine the change in angular momentum of the disk after a known time of 5.0s? A) Force probe and protractor B) Force probe, protractor, and motion sensor C) Electronic balance and force probe D) Electronic balance, force probe, and motion sensor

A) Force probe and protractor

A disk rotates about its center with an angular speed of 30 rad/s. An identical disk is held at rest above the rotating disk and is then gently dropped on the rotating disk, as shown in Figure 1. The two-disk system then rotates with a common angular speed ω1. A third identical disk is held at rest above the two-disk system. The third disk is gently dropped on the rotating two-disk system, as shown in Figure 2. The three-disk system then rotates with a common angular speed ω2. What is value of ω2? A) 0 rad/s0 rad/s B) 10 rad/s10 rad/s C) 20 rad/s20 rad/s D) 30 rad/s

10 rad/s

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? A) 18 Nm clockwise B) 18Nm counterclockwise C) 50 Nm clockwise D) 50 Nm counterclockwise

18 Nm counterclockwise

A rod is initially at rest on a rough horizontal surface. Three forces are exerted on the rod with the magnitudes and directions shown in the figure. The force exerted in the center of the rod is an equidistant 0.5m from both ends of the rod. If friction between the rod and the table prevents the rod from rotating, what is the magnitude of the torque exerted on the rod about its center from frictional forces? A) 0 Nm B) 10 Nm C) 20 Nm D) 30 Nm

20 Nm

A uniform rod is at rest on a horizontal surface. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. Path X and path Z are directed toward the center of mass of the rod. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. In each case, the time of collision between the sphere of clay and the rod is time t0. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. Frictional forces are considered to be negligible. 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. B) The system will rotate in the counterclockwise direction with a constant angular speed. C) The system will rotate in the clockwise direction with a changing angular speed. D) The system will rotate in the counterclockwise direction with a changing angular speed.

A) The system will rotate in the clockwise direction with a constant angular speed.

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. B) Yes, because the angular momentum is increasing with time. C) No, because the slope of the best-fit line is positive. D) No, because the area under the best-fit line is increasing with time for a specific time interval.

A) Yes, because the slope of the best-fit line is constant.

During an experiment, students collect data about the angular momentum of a rigid, uniform spinning wheel about an axle as a function of time, which was used to create the graph that is shown. A frictional torque is exerted on the wheel. A student makes the following statement about the data. "The frictional torque exerted on the wheel is independent of the wheel's angular speed." Does the data from the graph support the student's statement? Justify your selection. A) Yes, because the slope of the line is constant. B) Yes, because the angular momentum of the wheel decreases as time increases. C) No, because the area bound by the curve and the horizontal axis from 0 s0 s to 10 s10 s is a positive value. DNo, because the data does not provide information about the relationship between net torque and angular speed.

A) Yes, because the slope of the line is constant.

A uniform disk with mass M0 and radius R is mounted on a vertical axis so that it can rotate freely in a horizontal plane. The rotational inertia of the disk is I0. The disk is initially at rest. If force F0 is exerted tangentially to the rim of the disk for time interval Δt, the final angular momentum of the disk is L0. Consider a second disk that has the same mass M0 as the first disk, but its radius is 2R. The rotational inertia of this disk is 4I0. If the same force F0 is exerted tangentially to the rim of the disk for the same time interval Δt, then the final angular momentum of the second disk would be A) L0 B) 2L0 C) 4L0 D) 8L0

B) 2L0

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 and sticks to the rod, and the clay-rod system rotates, as shown in Figure 2. Which of the following linear collisions is analogous to the rotational collision that is described? A) A block traveling in the positive direction collides with a second block that travels in the negative direction. After the collision, the two blocks move together with a common final speed. B) A block traveling in the positive direction collides with a second block that is at rest. After the collision, the two blocks move together with a common final speed. C) A block traveling in the positive direction collides with a second block that travels in the negative direction. After the collision, the blocks reverse their directions and travel with their original speeds. D) A block traveling in the positive direction collides with a second block that is at rest. After the collision, the two blocks move at different speeds in the same direction.

B) A block traveling in the positive direction collides with a second block that is at rest. After the collision, the two blocks move together with a common final speed.

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point's angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. How can the graph be used to determine the angular speed of the disk after 2s? Justify your selection. A) Determine the area bound by the line and the horizontal axis from 0s0s to 2s2s , because this area represents the final angular velocity of the point on disk. B) Determine the area bound by the line and the horizontal axis from 0s0s to 2s2s , because this area represents the change in the angular velocity of the point on disk. C) Determine the vertical-axis intercept, because this value represents the final angular velocity of the point on disk. D) Determine the slope of the line, because this value represents the change in the angular velocity of the point on disk.

B) Determine the area bound by the line and the horizontal axis from 0s0s to 2s2s , because this area represents the change in the angular velocity of the point on disk.

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. The students conduct the experiment and gather data about the net torque exerted on the door and angular acceleration of the door for several trials. They create a graph of the door's angular acceleration as a function of the net torque and sketch a best-fit line through the data. How can the students analyze the data to determine the rotational inertia of the door about its hinges? A) Determine the slope of the best-fit line. B) Determine the inverse of the slope of the best-fit line. C) Determine the horizontal intercept of the best-fit line. D) Determine the vertical intercept of the best-fit line.

B) Determine the inverse of the slope of the best-fit line.

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. A) The initial angular velocity of the disk, because this quantity is related to the angular impulse of the disk. 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. C) The mass of the disk, because this quantity is related to the rotational inertia of the disk. D) The radius of the disk, because this quantity is related to the rotational inertia of the disk.

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.

A student conducts an experiment in which data is collected about the net torque exerted on the edge of a disk as it rotates about its center as a function of time. The student creates the graph that is shown. Before the net torque is applied to the disk, it rotates in the positive direction. The student makes the following claim. "The change in angular momentum of the disk from 0 s to 4 s is in the positive direction." Which of the following statements is correct about the student's evaluation of the data from the graph? Justify your selection. A) The student is correct, because there is a greater maximum magnitude of positive net torque exerted on the disk than the maximum magnitude of positive net torque exerted on the disk. B) The student is correct, because the area bound by the data and the horizontal axis from 0 s0 s to 4 s4 s is positive. C) The student is incorrect, because the slope of the line from the data point at 0 s0 s and the data point at 4 s4 s is negative. D) The student is incorrect, because the net torque at 4 s4 s is zero.

B) The student is correct, because the area bound by the data and the horizontal axis from 0 s0 s to 4 s4 s is positive.

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? A) 0 B) 1.2 kg m2/s C) 3 kg m2/s D) 6 kg m2/s

C) 2 kg m2/s

A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3rad/s clockwise. The graph shows the point's angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. What is the angular displacement of the point after 10s? A) 57 radians B) 63 radians C) 270 radians D) 330 radians

C) 270 radians

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? A) Determine the average value of the net force from 0 s0 s to 4 s4 s and multiply the result by the radius of the disk. B) Determine the average value of the net force from 0 s0 s to 4 s4 s and divide the result by the radius of the disk. 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. D) Determine the area bound by the best fit curve and the horizontal axis from 0 s0 s to 4 s4 s and divide the result by the radius of the disk.

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.

Three disks are concentrically attached to one another, and four rods of negligible mass are attached to the outer disk. Identical objects of mass Mo can be attached to the rods, and their positions on the rods can be adjusted. The disks, rods, and objects form a system that freely rotates around a central axis that is perpendicular to the plane of the page. The objects are initially a distance D away from the axis of rotation. A constant force F0 is applied tangent to the second disk, as shown in the figure. How can the system be changed so that the change in angular momentum of the system per unit of time is increased? A) Move the objects of mass M0 farther away from the axis of rotation. B) Move the objects of mass M0 closer to the axis of rotation. C) Increase the magnitude of the net torque exerted on the system. D) Decrease the magnitude of the net torque exerted on the system.

C) Increase the magnitude of the net torque exerted on the system.

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? A) L will be greater after the collapse. B) L will be less after the collapse. C) L will be the same as before the collapse. D) The magnitude of L⃗ L→ will be the same as before the collapse, but the direction of the angular momentum will be in the opposite direction after the collapse.

C) L will be the same as before the collapse.

A uniform rod is at rest on a horizontal surface. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. Path X and path Z are directed toward the center of mass of the rod. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. In each case, the time of collision between the sphere of clay and the rod is time t0. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. Frictional forces are considered to be negligible. 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 chagne

A planet of mass Mp orbits a star of mass Ms in the path shown above as a result of Newton's law of universal gravitation. Which of the following predictions correctly describes the angular momentum of the planet-star system and the angular velocity of the planet about the axis of revolution as it travels from position X to position Z? A) The angular momentum of the system increases, and the angular velocity of the planet increases. B) The angular momentum of the system increases, and the angular velocity of the planet remains constant. C) The angular momentum of the system remains the same, and the angular velocity of the planet increases. D) The angular momentum of the system remains the same, and the angular velocity of the planet remains the same.

C) The angular momentum of the system remains the same, and the angular velocity of the planet increases.

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. A) The change in the object's angular momentum for a given time interval remains the same throughout the experiment. This is because the slope of the best-fit line in Figure 1 is constant. B) The change in the object's angular momentum for a given time interval remains the same throughout the experiment. This is because the net torque and angular momentum increase in Figure 1 and Figure 2, respectively. 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. D) 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 net torque is nonzero in Figure 1.

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.

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. A) The student is correct, because the angular momentum of the disk decreases as time increases. B) The student is correct, because the slope of the best-fit curve of the graph remains constant. C) The student is incorrect, because the graph shows that the net torque exerted on the disk is constant as time increases. D) The student is incorrect, because the graph does not contain enough information to make a direct connection between the angular momentum of the disk and the angular acceleration of the disk.

C) The student is incorrect, because the graph shows that the net torque exerted on the disk is constant as time increases.

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? A) A block traveling in the positive direction collides with a second block that travels in the negative direction. After the collision, the two blocks move together with a common final speed. B) A block traveling in the positive direction collides with a second block that is at rest. After the collision, the two blocks move together with a common final speed. C) A block traveling in the positive direction collides with a second block that travels in the negative direction. After the collision, the blocks reverse their directions and travel with their original speeds. 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.

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.

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. A) 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. B) A stopwatch to measure the time interval during which the force is applied and a meterstick to measure the radial distance from the door's hinges to the location where the force is applied. C) A force probe to measure the applied force on the door, and a stopwatch to measure the time interval during which the force is applied, and a meterstick to measure the radial distance from the door's hinges to the location where the force is applied. 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.

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.

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 0s0s to 6s6s, because the shape of the curve on the graph will be a right triangle and the area can be directly determined.

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? A) The angular momentum of the skater is greatest in Figure 1. B) The angular momentum of the skater is greatest in Figure 2. C) The angular momentum of the skater is greatest in Figure 3. D) The angular momentum of the skater is the same in all figures.

D) The angular momentum of the skater is the same in all figures.

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. The students must determine how to test the relationship between a torque exerted on the door and the change in the angular velocity of the door. All frictional forces are considered to be negligible. How should the experiment be conducted to test the relationship between the torque exerted on the door and the change in the door's angular velocity in a way that minimizes experimental uncertainty? A) The students should perform several trials, applying the same force at the same vertical distance from the floor. B) The students should perform several trials, applying the same force at different vertical distances from the floor. C) The students should perform several trials, applying the same force at the same horizontal distance from the hinges. D) The students should perform several trials, applying the same force at different horizontal distances from the hinges.

D) The students should perform several trials, applying the same force at different horizontal distances from the hinges.