Physics

Angular and Linear Quantities: A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child?

8.05 m/s^2

Work and Power: The torque required to turn the crank on an ice cream maker is 4.50 N ∙ m. How much work does it take to turn the crank through 300 full turns?

8480 J

Angular Quantities: What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

85.14 rad/s

The two ends of the barbell shown in (Figure 1) are made of the same material. Which of the points shown is at the barbell's center of gravity?

A

Vector Nature of Angular Quantities: As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity vector of the door as you open it?

down

A nut needs to be tightened with a wrench. Which force shown in the figure will apply the greatest torque to the nut?

figure C, downwards at end

Torque: Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

force C

Angular Momentum: A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,

her moment of inertia increases and her angular speed decreases.

Angular Momentum: A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.)

his total kinetic energy

Rotational Kinetic Energy: A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is

less than the total kinetic energy of the cylinder.

An object's angular momentum is proportional to its __________.

moment of inertia

Rotational Kinetic Energy: Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

neither the mass nor the radius of the sphere.

If there is no slipping, a frictional force must exist between the wheels and the ground. In what direction does the frictional force from the ground on the wheels act? Take the positive x direction to be to the right.

positive x direction

Rotational Kinetic Energy: A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?

sphere

Rotational Kinetic Energy: A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?

sphere, disk, hoop

A net torque applied to an object causes __________.

the angular velocity of the object to change

Torque: Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge?

the first force (applied perpendicular to the door)

Torque: Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?

the first force (at the midpoint)

Angular Momentum: A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

the moment of inertia of the system decreases and the angular speed increases.

Rotational Kinetic Energy: Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

the radius of the sphere.

Moment of inertia is __________.

the rotational equivalent of mass

Rotational Kinetic Energy: A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?

the sphere

Angular Momentum: If the answer to your calculation has units of kg ∙ m2/s2, what type of quantity could it be? (There could be more than one correct choice.)

work

Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates with constant speed 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. What is the magnitude of the angular acceleration of the salad spinner as it slows down?

αα =8.38 radians/s^2

Angular Quantities: At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

22 rad/s

Equilibrium: If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

True

Angular Momentum: If the answer to your calculation has units of kg ∙ m2/s, what type of quantity could it be? (There could be more than one correct choice).

angular momentum

What is the net torque about the axle on the pulley in (Figure 1)? (4.0 cm, 20 N left, 30 N right

-0.20 Nm

The 2.6 kg, uniform, horizontal rod in (Figure 1) is seen from the side. (25 cm, 75 cm). What is gravitational torque?

-6.4 N⋅m

Rotational Dynamics: In a laboratory experiment, a student brings up the rotational speed of a flywheel to 30.0 rpm. She then allows it to slow down on its own, and counts 240 revolutions before the apparatus uniformly comes to a stop. The moment of inertia of the flywheel is 0.0850 kg ∙ m2. What is the magnitude of the retarding torque on the flywheel?

0.000278 N ∙ m

Angular Quantities: An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular speed in rad/s?

0.0011 rad/s

Rotational Dynamics: A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg ∙ m2, and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque?

0.00750 N ∙ m

Rotational Kinetic Energy: A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy?

0.092 J

Moment of Inertia: A majorette fastens two batons together at their centers to form an X shape. Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end. What is the moment of inertia of this baton about an axis through the center of the X?

0.36 kg⋅m^2

Constant Angular Acceleration: When an old LP turntable was revolving at 33 1/3 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds.What was the magnitude of its angular acceleration (in rad/s2) as it slowed down?

0.63 rad/s^2

Angular Quantities: When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan?

0.74 rad/s^2

Angular and Linear Quantities: A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping?

0.90 rad/s^2

Torque: As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

1

Equilibrium: A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

1.0 m

Equilibrium: A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h = 4.0 m, as shown in the figure. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40. An 80-kg bucket is suspended from the top rung of the ladder, just at the wall. What is the magnitude of the force that the ladder exerts on the wall?

740 N

Specifications require the oil filter for your car to be tightened with a torque of 30 N⋅m. You are using a 15-cm-long oil filter wrench, and you apply a force at the very end of the wrench in the direction that produces maximum torque.

200 N

Equilibrium: A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.30. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

1.4 m

Through how many revolutions did it turn while stopping?

1.5 rev

Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.1 kg *m^2 and for arms and legs in is 0.90 kg *m^2 . If she starts out spinning at 6.0 rev/s , what is her angular speed (in rev/s) when her arms and one leg open outward?

1.7 rev/s

Equilibrium: As shown in the figure, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle θ = 49° with the bar. The bar is uniform and weighs 66.5 N. What distance x from the hinge should a 10.0 kg mass be suspended for the tension in the rope to be 177 N?

10 m

Rotational Dynamics: The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

10.4 rad/s^2

Angular and Linear Quantities: A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

100 rad/s

Equilibrium: An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is FM in the figure) in the upper arm exert on the lower arm?

1000 N

The lightweight wheel on a road bike has a moment of inertia of 0.097 kg⋅m^2. A mechanic, checking the alignment of the wheel, gives it a quick spin; it completes 5 rotations in 2.4 s. To bring the wheel to rest, the mechanic gently applies the disk brakes, which squeeze pads against a metal disk connected to the wheel. The pads touch the disk 7.1 cm from the axle, and the wheel slows down and stops in 1.5 s. What is the magnitude of the friction force on the disk?

12 N

Equilibrium: A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

127 g

What is the net torque on the bar shown in (Figure 1), about the axis indicated by the dot? Suppose that F = 19 N. (25 cm, 75 cm, 8 N force right)

14 Nm

A frictionless pulley, which can be modeled as a 0.83 kg solid cylinder with a 0.35 m radius, has a rope going over it, as shown in (Figure 1). (pully: 12 N left, 10 N right). The tensions in the rope are 12 N and 10 N. What is the angular acceleration of the pulley?

14 rad/s^2

Torque: The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

16 Nm

We can model a small merry-go-round as a uniform circular disk with mass 88 kg and diameter 1.8 m. How many 22 kg children need to ride the merry-go-round, standing right at the outer edge, to double the moment of inertia of the system?

2 N

The 510 g bar is rotating as shown in (Figure 1). 2 meter stick, 120 rpm

2.1 kg*m^2/ s

Equilibrium: A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center?

2.1 m

Rotational Kinetic Energy: A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N, causing the pulley to rotate. What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley?

2.36 m/s

A school has installed a modestly-sized wind turbine. The three blades are 4.1 m long; each blade has a mass of 45 kg. You can assume that the blades are uniform along their lengths. When the blades spin at 240 rpm, what is the kinetic energy of the blade assembly?

2.4×10^5 J

A typical compact disk has a mass of 15 g and a diameter of 120 mm. What is its moment of inertia about an axis through its center, perpendicular to the disk?

2.7×10^−5kg⋅m^2

The moon's mass is 7.4×10^22 kg and it orbits 3.8×10^8m from the earth with a period of 27.3 days.

2.8×10^34 kg*m^2/s

Equilibrium: A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

20 N ∙ m

Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates with constant speed 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. How long does it take for the salad spinner to come to rest?

3 seconds

The turntable in a microwave oven has a moment of inertia of 0.041 kg *m^2 and is rotating once every 4.9 s. What is its kinetic energy?

3.4×10^−2 J

If the moment of inertia of the diver in a straight position is 14 kg*m^2 and in a tucked position is 4.0 kg*m^2, by what factor does her angular speed increase?

3.5

Angular and Linear Quantities: A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?

3.50 m/s

Rotational Kinetic Energy: A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill?

3.57 m

Torque: The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench?

300 N

If Luis pulls straight down on the end of a wrench that is tilted θ = 30∘ above the horizontal and is r = 39 cmcm long, what force must he apply to exert a torque of -11 N⋅m ?

33 N

Rotational Dynamics: A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?

4.78 kg ∙ m^2

Torque: A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is horizontal?

43 N ∙ m

The 2.3 kg, 5.4-cm-diameter disk is rotating as shown in (Figure 1). 600 rpm clockwise. What is the angular momentum of the disk about the axle?

5.3×10^-2 kg*m^2/s

Rotational Dynamics: A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kg ∙ m2 and a radius of 15.0 cm. A mass of 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710-g tile?

5.59 N

What is the net torque about on the bar shown in (Figure 1) about the axis indicated by the dot? Suppose that ϕ= 50∘ and θ= 80∘. (25 cm, 75 cm, 8 N left, 10 N right)

5.9 Nm

Rotational Kinetic Energy: A wheel having a moment of inertia of 5.00 kg ∙ m2 starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

57.6 J

A professor's office door is 0.86 mm wide, 2.0 mm high, and 4.0 cm thick; has a mass of 25 kg; and pivots on frictionless hinges. A "door closer" is attached to the door and the top of the door frame. When the door is open and at rest, the door closer exerts a torque of 5.2 N*m. What is the least force that you need to apply to the door to hold it open?

6 N

A small grinding wheel has a moment of inertia of 4.0×10−5 kg*m^2. What net torque must be applied to the wheel for its angular acceleration to be 150 rad/s^2 ?

6.0×10^−3 Nm

A 250 g , 23-cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1800 rpm in 5.0 s ?

6.2×10^2 Nm

An object's moment of inertia is 2.0 kg⋅m^2 . Its angular velocity is increasing at the rate of 3.3 rad/s per second. What is the net torque on the object?

6.6 Nm

Rotational Dynamics: A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at 1.6 rad/s2 what is the mass of the disk?

60 kg

A 2.4 kg , 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 400 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rpm, just after this event?

60 rpm

Angular Quantities: Through how many degrees does a 33 rpm turntable rotate in 0.32 s?

63°

Torque: A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque about the pivot point produced by this force?

7.6 N ∙ m

Equilibrium: A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground?

740 N

Equilibrium: A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550-N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B, in the two wires?

A = 910 N, B = 840 N

Moment of Inertia: The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

B

Rotational Kinetic Energy: Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?

Both are equal.

Rotational Kinetic Energy: Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?

Both reach the bottom at the same time.

Equilibrium: If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.

False

A student gives a steady push to a ball at the end of a massless, rigid rod for 1 s, causing the ball to rotate clockwise in a horizontal circle as shown in (Figure 1). The rod's pivot is frictionless.

Graph: down to negative 1, then constant

Angular Momentum: A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)

Her angular momentum remains constant.

Rotational Kinetic Energy: Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Translational kinetic energy is larger.

Angular and Linear Quantities: Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.)

Jacques and Ahmed have the same angular speed.

Angular Momentum: When is the angular momentum of a system constant?

Only when no net external torque acts on the system.

A baseball bat has a thick, heavy barrel and a thin, light handle. What should you do if you want to hold a baseball bat on your palm so that it balances vertically?

Put the end of the handle in your palm, with the barrel up.

Two horizontal rods are each held up by vertical strings tied to their ends. Rod 1 has length L and mass M; rod 2 has length 2L and mass 2M. Each rod then has one of its supporting strings cut, causing the rod to begin pivoting about the end that is still tied up. Which rod has a larger initial angular acceleration?

Rod 1

(pully with 2 masses) Which of the following statements correctly describes the system shown in the figure?

The angular acceleration of the pulley is nonzero.

How is the angular displacement θ related to the angular velocity ω?

The change in the angular displacement over the change in time is the angular velocity.

(pully with 2 masses) What happens when block B moves downward?

The cord's tension on the right side of the pulley is higher than on the left side.

Rotational Kinetic Energy: A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping?

The disk

On what does the magnitude of an applied torque depend?

The magnitude of the force, The orientation of the force, The distance between the point of force application and the axis of rotation of the object.