Exam 8: Rotational Motion

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s. (a) Through what angle does the bowling ball turn as it travels the length of the lane? (b) What is the angular speed of the bowling ball? (c) Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have. (d) Calculate the tangential acceleration of a point on the surface of the bowling ball.

A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through one-half of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the one-half revolution?

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?

A ball in the shape of a uniform spherical shell (like a soccer ball) of mass 1.5 kg and radius 15 cm rolls down a $35 ^ { \circ }$ incline that is 6.0 m high, measured vertically. The ball starts from rest, and there is enough friction on the incline to prevent slipping of the ball. (a) How fast is the ball moving forward when it reaches the bottom of the incline, and what is its angular speed at that instant? (b) If there were no friction on the incline, how fast would the ball be moving forward and what would be its angular speed at the bottom?

When is the angular momentum of a system constant?

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius $R _ { 1 } = 1.0$ m exerts a force of magnitude $F _ { 1 } = 5.0 \mathrm {~N}$ to the right. A second rope wrapped around another section of radius $R _ { 2 } = 0.50 \mathrm {~m}$ exerts a force of magnitude $F _ { 2 } = 6.0 \mathrm {~N}$ downward. What is the angular acceleration of the cylinder?

NASA puts a satellite into space that consists of two small 32-kg balls connected by a 12-m long light cable, as shown in the figure. The entire system is initially rotating at 4.0 rpm about an axis perpendicular to the cable at the center of mass. Motors in each mass reel out more cable so that the masses double their separation to 24 m. (a) What is the final rotational speed (in rpm) of the balls? (b) If the initial rotational kinetic energy of the system was K, what is the final rotational $\text { kinetic energy in terms of } K \text { ? }$

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?

A 24.5-kg child is standing on the outer edge of a horizontal merry-go-round that has a moment of inertia of $989 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ about a vertical axis through its center and a radius of 2.40 m. The entire system (including the child) is initially rotating at 0.180 rev/s. Find the angular velocity if the child moves to a new position 1.10 m from the center of the merry-go-round.

A light-weight potter's wheel, having a moment of inertia of $24 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ is spinning freely at 40.0 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm, what is the mass of the clay?

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

When you ride a bicycle, in what direction is the angular velocity of the wheels?

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O , as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius $R _ { 1 } = 1.0$ m exerts a force of magnitude $F _ { 1 } = 5.0 \mathrm {~N}$ to the right. A second rope wrapped around another section of radius $R _ { 2 } = 0.50 \mathrm {~m}$ exerts a force of magnitude $F _ { 2 } = 6.0 \mathrm {~N}$ downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

If the answer to your calculation has units of $\mathrm { kg } \cdot \mathrm { m } ^ { 2 } / \mathrm { s } ^ { 2 }$ What type pf quantity could it be? (There could be more than one correct choice.)

The drive chain in a bicycle is applying a torque of $0.850 \mathrm {~N} \cdot \mathrm { m }$ 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?

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

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x -axis, and (b) about the y -axis?

In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses.

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of $2.25 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ If he pulls in his arms so his moment of inertia decreases to $1.80 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ angular speed? what will be his new