A high-speed drill reaches 2000 rpm in 0.50 s. What is the magnitude of the drill's angular acceleration?

A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. What is the speed of the tip of a blade 10 s after the fan is turned off?

A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. Through how many revolutions does the fan turn while stopping?

An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60 rpm to 90 rpm in 10 s. What is the tangential acceleration of a tooth on the sprocket?

Two balls are connected by a 150-cm-long massless rod. The center of mass is 35 cm from a 75 g ball on one end. What is the mass attached to the other end?

What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?

The three 200 g masses in FIGURE EX12.11 are connected by massless, rigid rods. What is the triangle's kinetic energy if it rotates about the axis at 5.0 rev/s?

The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. Find the coordinates of the center of mass.

The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. Find the moment of inertia about a diagonal axis that passes through masses B and D.

The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. Find the coordinates of the center of mass.

The three masses shown in FIGURE EX12.15 are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page.

A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation on its hinges?

A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door’s moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge?

A 12-cm-diameter DVD has a mass of 21 g. What is the DVD’s moment of inertia for rotation about a perpendicular axis through its center?

A 12-cm-diameter DVD has a mass of 21 g. What is the DVD's moment of inertia for rotation about a perpendicular axis through the edge of the disk?

In FIGURE EX12.19, for what value of X_axle will the two forces provide 1.8 Nm of torque about the axle?

A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?

An object's moment of inertia is 2.0 kg m². Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?

An object whose moment of inertia is 4.0 kg m² is rotating with angular velocity 0.25 rad/s. It then experiences the torque shown in FIGURE EX12.25. What is the object's angular velocity at t = 3.0s?

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What net torque will bring the balls to a halt in 5.0 s?

A 12-cm-diameter, 600 g cylinder, initially at rest, rotates on an axle along its axis. A steady 0.50 N force applied tangent to the edge of the cylinder causes the cylinder to reach an angular velocity of 500 rpm in 2.0 s. What is the magnitude of the frictional torque between the cylinder and the axle?

The object shown in FIGURE EX12.29 is in equilibrium. What are the magnitudes of ${\overrightarrow{F_1}}_{}$ and ${\overrightarrow{F_2}}_{}$?

A 5.0 kg cat and a 2.0 kg bowl of tuna fish are at opposite ends of the 4.0-m-long seesaw of FIGURE EX12.32. How far to the left of the pivot must a 4.0 kg cat stand to keep the seesaw balanced?

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. What is the speed of a point at the top edge of the tire?

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. What is the speed of a point at the bottom edge of the tire?

An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom. What is the sphere’s angular velocity at the bottom of the incline?

An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom. What fraction of its kinetic energy is rotational?

A solid sphere of radius R is placed at a height of 30 cm on a 15° slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere's speed at the bottom?

Evaluate the cross products and A ✕ B and C ✕ D.