Physics Clutch

The graph below represents the motion of a moving object. The graph in Figure 4-3 shows an angular acceleration of:

0.2 rad/s

Each of the four graphs pictured in the diagram below represent the motion of four different objects. Which graph in Figure 3-1 represents an object with non-zero uniform angular speed?

1 (constant slope)

Cindy, who weighs 600 newtons, sits balanced on a seesaw 3.0 meters from her sister Sandra, who weighs 300 newtons. If the seesaw has negligible mass compared to the two sisters, the position of the balance point of the seesaw is about-

1 meter from Cindy

A graph of the angular velocity w as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1-3, are shown. During which of the following time intervals is the net torque applied to the object a constant value?

1, 2, and 3

An inclined track is secured to a table. The height of the highest point of the track above the tabletop is h1. The height from the tabletop to the floor is h2. A block of mass M is released from rest and slides down the track such that all frictional forces are considered to be negligible. The block leaves the track horizontally and strikes the ground at a distance D from the edge of the track as shown. Which of the following statements is correct about the scenario? Select two answers.

1. The total mechanical energy of the block-Earth system remains constant. 2. The total mechanical energy of the system containing only the block increases from the moment of release to the moment it strikes the ground.

The rigid body shown in the diagram above 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 w. 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?

1/8

A passenger compartment of a rotating amusement park ride contains a bench on which a book of mass m is placed, as indicated by the dot in the left figure above. The compartment moves with a constant angular speed about the center of the ride along a circular path of radius R. The bench remains horizontal throughout the compartment's motion. The right figure above shows a magnified view of the compartment. The graph below shows the horizontal component of the book's position as a function of time, where the +x direction is to the right. Which of the following represents the period of revolution of the book?

120 s

A graph of the angular velocity w as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1-3, are shown. During which of the following time intervals is the angular speed a constant value (select the option that has all the included time intervals)

2

Each of the four graphs pictured in the diagram below represents motion of four different objects. Which graph in Figure 3-1 represents an object whose angular speed is increasing?

2

The graph below represents the motion of a moving object. The initial angular speed (w0) shown in Figure 4-3 is:

2.0 rad/s

A .5 kg cart moves on a straight horizontal track. The graph of the velocity vx versus time t for the cart is given below. During which of the following time intervals is the cart moving at a constant speed?

20-25 s, 12-17 s

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

2FR

Each of the four graphs pictured in the diagram below represents the motion of four different objects. Which graph in Figure 3-1 represents an object whose angular speed is decreasing to zero?

3 (slowly tapering off)

A passenger compartment of a rotating amusement park ride contains a bench on which a book of mass m is placed, as indicated by the dot in the left figure above. The compartment moves with a constant angular speed about the center of the ride along a circular path of radius R. The bench remains horizontal throughout the compartment's motion. The right figure above shows a magnified view of the compartment. The graph below shows the horizontal component of the book's position as a function of time, where the +x direction is to the right. Which of the following times is the book have a magnitude of velocity equal to 0 m/s in the x-direction?

30 s

A passenger compartment of a rotating amusement park ride contains a bench on which a book of mass m is placed, as indicated by the dot in the left figure above. The compartment moves with a constant angular speed about the center of the ride along a circular path of radius R. The bench remains horizontal throughout the compartment's motion. The right figure above shows a magnified view of the compartment. The graph below shows the horizontal component of the book's position as a function of time, where the +x direction is to the right. Which of the following times is the book at its amplitude in the x-direction?

30 s

Each of the four graphs pictured in the diagram below represents the motion of four different objects. Which graph in Figure 3-1 represents an object whose angular speed is zero?

4 (flat line)

A bowling ball of mass M and radius R whose moment of inertia about its center is (2/5)MR^2, 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:

7v squared/10g

A .5 kg cart moves on a straight horizontal track. The graph of the velocity vx versus time t for the cart is given below. At which of the following times does the cart return back to its initial position?

8 s

A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3v, when it collides with a larger block of mass 1.5M at rest at the bottom of the incline. The larger block moves to the right at a speed 2v immediately after the collision. Express your answers to the following questions in terms of the given quantities and fundamental constants. Which of the following is the height, h, of the ramp?

9(v0)²/2g

Four students are spinning on a merry-go-round. A is on edge, B .2 m, C .4 m, D on axis of rotation. Which student has the highest kinetic energy?

A (the one on the edge)

A uniform bar, of mass M, with seven evenly spaced holes is held by sliding the bar over a horizontal peg through one of the seven holes. The peg passes through hole C and into a wall, the mass of the bar is equal to the mass of the cylinder, and the location of the center of mass of the bar is at the center of hole D. At t=0, the cylinder hangs from a hook placed through hole B as shown above and the system is released. Frictional forces are negligible. Two additional cylinders, identical to the one hanging at location B, are to be hung from the bar. At which of the following locations should they be placed so the bar will be in rotational equilibrium?

A and E

A .5 kg cart moves on a straight horizontal track. The graph of velocity vx versus time t for the cart is given below. During which of the following time intervals is the cart moving at a constant acceleration?

All

Four students are spinning on a merry-go-round. D is on edge, C .2 meters, B .4 meters, A on axis of rotation. Which student has the highest angular speed?

All equal

In a classroom at time t = 0 , a sphere is thrown upward at a 45° angle to the horizontal. At time t1, while the sphere is still rising, it bounces off the ceiling elastically and with no friction. Which of the following pairs of graphs could represent the sphere's horizontal velocity and vertical velocity as functions of time t?

B

The figure above shows a uniform meterstick that is set on a fulcrum at its center. A force of magnitude F toward the bottom of the page is exerted on the meterstick at the position shown. At which of the labled positions must an upward force of magnitude 2F be exerted on the meterstick to keep the meterstick in equilibrium.

B

Object X travels across a horizontal surface and collides with object Y. The velocity as a function of time for object X and object Y before, during, and after the collision is shown in the graph. Both objects have a mass of 2kg. Which of the following correctly describes the momentum p⃗ of the system and the kinetic energy K of the system?

B (momentum conserved, kinetic energy not conserved)

A satellite travels around the Sun in an elliptical orbit as shown above. As the satellite travels from point X to point Y, which of the following is true about the magnitudes of the tangential speed and linear acceleration?

B (tangential speed increases, linear acceleration increases)

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 (Angular momentum remains constant, kinetic energy increases)

A vehicle travels at a constant speed around a circular curve. Part of the curve is covered with ice. On the ice, the frictional force holding the tires to the road is zero. Which arrow best represents the vehicle's velocity when it reaches the ice?

C (straight arrow)

Four students are spinning on a merry go round. Student D is on the edge, C is .2 m, B is .4 m, and A is on the axis of rotation. Which student has the greatest friction force applied to them by the merry go round?

D (on the edge)

Four students are spinning on a merry-go-round. D is on edge, C .2, B .4, A on axis of rotation. Which student has the highest linear speed?

D (student on edge)

An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.

Determine the slope of the line from 0 to 2 s, because the slope represents change in w/change in t

The horizontal turntable shown above rotates at a constant rate. As viewed from above, a coin on the turntable moves counterclockwise in a circle as shown. Which of the following vectors best represents the direction of the frictional force exerted on the coin by the turntable when the coin is in the position shown?

Downward arrow

Ball A and Ball B are each thrown horizontally from the same height above level ground. Ball B has a greater initial speed after leaving the thrower's hand. How do the accelerations of the balls and the times it takes them to hit the ground compare? (air resistance is negligible)

E (equal for acceleration and equal for time of flight)

An elevator carrying a person of mass m is moving upward and slowing down. How does the magnitude F of the force exerted on the person by the elevator floor compare with the magnitude mg of the gravitational force?

F<mg

An object that is static equilibrium when which of the following conditions of equilibrium is achieved?

First and second

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 above. Which of the following quantities must be the same for the disk-rod system before and after the collision? I. Linear momentum II. Angular momentum III. Kinetic Energy

I and II only

When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?

Inertia

A uniform bar, of mass M, with seven evenly spaced holes is held by sliding the bar over a horizontal peg through one of the seven holes. The peg passes through hole C and into a wall, the mass of the bar is equal to the mass of the cylinder, and the location of the center of mass of the bar is at the center of hole D. At t=0, the cylinder hangs from a hook placed through hole B as shown above and the system is released. Frictional forces are negligible. Which of the following best describes the motion of the bar after t=0?

It will not change its current state of motion.

A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force is applied at the other end, at an angle to the rod. IF F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?

Lsin(-)

A universal horizontal beam of mass M and length L is attached to a hinge at point P, with the opposite end supported by a cable, as shown in the figure. The angle between the beam and the cable is theta. What is the magnitude of the torque that the weight of the beam exerts on the beam?

MgL/2

Which of the following will INCREASE the moment of inertia of an object?

Moving some of the object's mass farther from the center of rotation

A hula hoop of mass M and radius R rolls on a level surface without slipping. If the angular velocity of the wheel is w, what is its angular momentum ?

MwR²

Four students are spinning on a merry go round. Student A is on the edge, B is .2 m, C is .4 m, and D is on the axis of rotation. Which student has the highest moment of inertia>

Student A (on edge)

A .5 kg ball is spun in a vertical circle at a constant speed of 4 m/s. Which of the following would be the correct FBD for the ball at the top of the circle?

Tension and Weight pointing down

A .5 kilogram ball is spun in a vertical circle at a constant speed of 4 m/s. Which of the following would be the correct FBD for the ball at the bottom of the circle?

Tension arrow up weight arrow down

Which of the following statements is correct?

The farther the center of mass of an object is from the axis of rotation, the greater the object's moment of inertia is.

A ball is moved from Earth to a planet that has a gravitational acceleration that is double that of Earth. How does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball when it is on Earth?

The gravitational force on the ball when it is on the new planet is double the force on the ball when it is on Earth.

An object attached to one end of a string moves in a circle at constant speed. Which of the following is correct?

The object is accelerating as it moves.

A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. A portion of the recorded data is shown in the figure above. The acceleration of the object at 0.9s is most nearly equal to which of the following?

The slope of the tangent line to a best-fit sinusoidal curve at 0.9s

A ball is tossed straight up and later returns to the point from which it was launched. If the ball is subject to air resistance as well as gravity, which of the following statements is correct?

The speed at which the ball returns to the point of launch is less than its speed when it was initially launched.

A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above. The path is such that the lengths of its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time t during one trip around the path, beginning at point P ?

The square one rising at tQ

A block of mass M is released from rest at point 1, as shown in the figure. The block slides without frictional forces along the circular arc but encounters frictional forces as soon as it reaches the horizontal portion of the track at point 2. The block travels a distance D along the horizontal track before coming to rest at point 3. Consider the block-Earth system. In terms of the mechanical energy of the system, which of the following claims is correct and why?

The system is open, because there is a net force exerted on the block.

A square piece of plywood on a horizontal tabletop is subjected to the two horizontal forces shown above right. Where should a third force of magnitude 5 newtons be applied to put the piece of plywood into equilibrium?

The top left corner

A car initially travels north and then turns to the left along a circular curve. This causes a package on the seat of the car to slide toward the right side of the car. Which of the following is true of the net force of the package while it is sliding?

There is not enough force directed toward the center of the circle to keep the package from sliding.

If you cannot exert enough force to loosen a bolt with a wrench, which of the following should you do?

Use a wrench with a longer handle

A wheel of mass M and radius R rolls on a level surface without slipping. Which of the following statements about the velocity at the top (vtop), velocity at the center of the mass (vcm), and the velocity at the bottom (vbottom) are true?

Vtop>vcm>Vbottom

Four students are spinning on a merry go round. Student D is on the edge, C is .2 m, B is .4 m, and A is on the axis of rotation. Which student has the greatest angular displacement?

all equal

The total kinetic energy of a baseball thrown with a spinning motion is which of the following?

both the ball's linear and rotational speeds

As a spaceship from Earth goes toward the moon, the force it exerts on the Earth:

decreases

Torque is the rotational analogue of

force

A child rides a bicycle in a circular path with a radius of 4.0m. The tangential speed of the bicycle is 4.0 m/s. The combined mass of the bicycle and child is 80 kg. Use this information for the next three questions. What kind of force provides the centripetal force on the bicycle?

friction

In the figure above, according to Kepler's Second Law of Planetary Motion,

if change in t1=change in t2, then A1=A2

A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3v, when it collides with a larger block of mass 1.5M at rest at the bottom of the incline. The larger block moves to the right at a speed 2v immediately after the collision. Express your answers to the following questions in terms of the given quantities and fundamental constants. Which fo the following would best classify this collision?

inelastic

When an object is moving with uniform circular motion, the object's tangential speed

is constant.

The toy car shown in the figure above enters the vertical circular loop with an initial velocity and moves completely around the loop without friction. If the car has no means of self-propulsion, which of the following is true of the car's acceleration at the instant it is at point P ?

it has components both downward and toward the center of the circle

A uniform horizontal beam of mass M and length L0 is attached to a hinge at point P, with the opposite end supported by a cable, as shown in the figure. The angle between the beam and the cable is θ. Which of the following best describes the reaction force the wall applies on the beam at point P?

it is directed up and to the left

The toy car shown in the figure above enters the vertical circular loop with an initial velocity and moves completely around the loop without friction. IF the car has no means of self-propulsion, which of the following is true of the car's acceleration at the instant it is at the top of the circle?

it is directly toward the center of the circle

Rotational inertia is the rotational analogue for

mass

If a race car travels around corner #3 of the racetrack at three times the speed used on corner #2, the frictional force required to keep the car on the track must be:

nine times as great.

A .5 kg cart moves on a straight horizontal track. The graph of velocity vx versus time t for the cart is given below. At which of the following time intervals is the cart at rest for the entire interval?

none of these

A uniform horizontal beam of mass M and length L is attached to a hinge at Point P, with the opposite end supported by a cable as shown in the figure. The angle between the beam and the cable is theta. What is the magnitude of the net torque at Point P?

none of these

Four students are spinning on a merry go round. Student A is on the edge, B is .2 m, C is .4 m, and D is on the axis of rotation. If each student jumps off radially, parallel to the radius, what would happen to the rotation of the merry go round?

nothing

Four students are spinning on a merry go round. Student A is on the edge, B is .2 m, C is .4 m, and D is on the axis of rotation. If each student jumps off tangentially to the radius in the direction of motion, perpendicular to the radius, what would happen to the rotation of the merry go round?

slow down

A racing car is moving around the circular track of radius 50 meters shown above. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 2 meters per second squared. When viewed from above, the radial force is directed

south

A cylinder of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane is frictionless, what is the speed v, of the center of mass of the cylinder at the bottom of the incline?

sqrt 2gh

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

sqrt 4pia

Two friends say they cannot feel the gravitational attraction their teacher says they exert on one another. The reason they cannot feel it is because:

the friends' masses are so small that the gravitational force between them is insignificant.

A projectile fired into the air explodes and splits into two halves of equal mass that hit the ground at the same time. If the projectile had not exploded, it would have landed at point X, which is a distance R to the right of the launch point. After the explosion, one of the halves lands at point Y, which is a distance 2R to the right of the launch point. If air resistance is negligible, where did the other half land?

the launch point

The bar is initially motionless but is free to rotate around the peg with negligible friction. A ball of clay is dropped onto the bar in the position shown. The clay collides with and sticks to the bar. During this collision which of following is true about the clay-bar system?

the linear momentum is constant.

A 90-kilogram astronaut weighs 1/6 as much on the moon as on Earth because:

the mass of the moon is substantially less than the mass of the Earth.

A 5 kg object moving to the left collides with and sticks to a 10 kg object moving to the right. Which of the following is true of the motion of the combined objects immediately after the collision?

the motion cannot be determined without knowing the speeds of the objects before the collision.

An amusement park ride has two identical carriages that revolve around the center of the ride's axle, as shown in the figure. Both carts travel at a constant tangential speed at all points along the circular path. At what position is the total mechanical energy of the cart-cart-Earth system at its maximum value?

the total energy of the Earth-Ferris wheel ride is constant

Which of the following quantities measures the ability of a force to rotate or accelerate an object around an axis?

torque

A passenger compartment of a rotating amusement park ride contains a bench on which a book of mass m is placed, as indicated by the dot in the left figure above. The compartment moves with a constant angular speed about the center of the ride along a circular path of radius R. The bench remains horizontal throughout the compartment's motion. The right figure above shows a magnified view of the compartment. A the lowest point of the circular path, the book is moving only in the horizontal direction. In what direction, if any, is the net vertical force on the book?

up

A wedding ring of mass M and radius R 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

v squared/g

A hula hoop of mass M and radius R rolls on a level surface without slipping. If the angular velocity of the wheel is v and has a period of T, which of the following best describes the work done by friction on the hula hoop as it rolls?

zero

A graph of the angular velocity w as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1-3, are shown. Which of the following correctly compares the angular displacement θ of the object during each time period?

θ1=θ3<θ2

A cylinder of mass M, radius R, and rotaitonal inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane is frictionless, what is the speed v , of the center of mass of the cylinder at the bottom of the incline?

√2gh (all under radical)

A cylinder of mass M, radius R, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane has friction so that the cylinder rolls without slipping, what is the speed v of the center of mass at the bottom of the incline?

√4gh/3 (square root covers whole thing)