Question 1

A car is traveling at 20.0 m/s on tires with a diameter of 70.0 cm. The car slows to a rest after traveling 300.0 m. If the tires rolled without slipping, what was the magnitude of the average angular acceleration of the tires during the time the car slowed to a rest?

Accepted Answer

The answer of A car is traveling at 20.0 m/s...

Question 2

A thin hoop with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy?

Accepted Answer

Kinetic energy of a rotating hoop is given by (1/2) * I * w^2, where I is the moment of inertia and w is the angular speed. For a thin hoop, I = MR^2, where M is the mass and R is the radius. Plugging in the given values, we get:KE = (1/2) * (3.0 kg) * (0.1 m)^2 * (3.5 rad/s)^2 = 0.18 J

Question 3

A hoop is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts down a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00 m down the ramp?

Accepted Answer

The answer of A hoop is rolling without slipping along...

Question 4

A thin cylindrical shell is released from rest and rolls without slipping down an inclined plane that makes an angle of 30° with the horizontal. How long does it take it to travel 3.1 m?

Accepted Answer

The acceleration of a rolling object is (2/3)g sin(θ) for a thin cylindrical shell. Using the equation s = (1/2)at^2, solve for t: t = sqrt((2s)/(a)) = sqrt((2*3.1)/(2/3 * 9.8 * sin(30°))) ≈ 1.6 s.

Question 5

A solid sphere is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the sphere after it has rolled 3.00 m up the ramp?

Accepted Answer

The answer of A solid sphere is rolling without slipping...

Question 6

A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is the rotational inertia (moment of inertia) of the sphere about an axis passing through its center?

Accepted Answer

The answer of A hollow sphere has a mass of...

Question 7

A hoop is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00 m up the ramp?

Accepted Answer

The correct answer is A because the hoop's speed decreases as it rolls up the ramp due to the conversion of kinetic energy to potential energy.

Question 8

FIGURE 10-3 
-Fig. 10-3 illustrates a simplified roller bearing. The inner cylinder has a radius of 1.0 cm and is stationary. The outer hollow cylinder has a radius of 1.2 cm and is rotating at 8.0 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?

Accepted Answer

The small cylinders roll without slipping, meaning the linear speed at the contact point with both the inner and outer cylinders is the same. The outer cylinder's linear speed is 1.2 cm * 8.0 rpm = 9.6 cm/min. The small cylinders have a radius of 0.10 cm, so their angular speed is 9.6 cm/min / 0.10 cm = 96 rpm. However, they rotate in the opposite direction to the outer cylinder, so the net angular speed is 96 rpm / 2 = 48 rpm.

Question 9

A 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 3.5 rad/s. What is its kinetic energy?

Accepted Answer

The answer of A solid cylinder with a radius of...

Question 10

A uniform solid sphere of mass M and radius R rotates with an angular speed ω. What must be the angular speed of a uniform solid cylinder of mass M, radius R, and height 2R that has the same rotational kinetic energy of the sphere?

Accepted Answer

The answer of A uniform solid sphere of mass M...

Question 11

FIGURE 10-3 
-Fig. 10-3 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.2 cm and is stationary. The inner cylinder has a radius of 1.0 cm and is rotating at 11 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?

Accepted Answer

The answer of FIGURE 10-3 
-Fig. 10-3 illustrates a simplified...

Question 12

A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the bottom of the core with a constant speed of 25.0 cm/s, what is the speed of the spool?

Accepted Answer

The answer of A spool whose inner core has a...

Question 13

A mass M uniform solid cylinder of radius R and a mass M thin uniform spherical shell of radius R roll without slipping. If both objects have the same kinetic energy, what is the ratio of the speed of the cylinder to the speed of the spherical shell?

Accepted Answer

The answer of A mass M uniform solid cylinder of...

Question 14

Determine the moment of inertia of an equilateral triangular plate of mass M and sides L about an axis perpendicular to the plate that passes through one vertex of the triangle.

Accepted Answer

The answer of Determine the moment of inertia of an...

Question 15

The moment of inertia of a uniform rod (about its center) is given by I = M  /12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s?

Accepted Answer

The answer of The moment of inertia of a uniform...

Question 16

A homogeneous cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal. How fast is it moving after it has rolled 2.2 m down the plane?

Accepted Answer

The answer of A homogeneous cylinder is released from rest...

Question 17

FIGURE 10-3 
-Fig. 10-3 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.20 cm and is stationary. The inner cylinder has a radius of 1.00 cm and is rotating at 9.00 rpm. Between the two cylinders are several small cylinders with a radius of 0.100 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. How long does it take a small cylinder to complete a full revolution around the inner cylinder?

Accepted Answer

The small cylinder completes a full revolution around the inner cylinder in the time it takes the inner cylinder to rotate once. The inner cylinder rotates at 9.00 rpm, which means it takes 60/9 = 6.67 seconds for one full rotation. However, the small cylinder also rolls on the inner cylinder, effectively doubling the distance it travels, so it takes 6.67 * 2 = 13.34 seconds, which is approximately 14.7 seconds.

Question 18

A piece of thin wire of mass m and length 3a is bent into an equilateral triangle. Find the rotational inertia (moment of inertia) of the wire when it is rotating about an axis perpendicular to the plane of the triangle and passing through one of its vertices.

Accepted Answer

The answer of A piece of thin wire of mass...

Question 19

A solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25.0° with the horizontal. What is the speed of the disk after it has rolled 3.00 m, measured along the plane?

Accepted Answer

To solve the problem, we can use conservation of energy. The initial potential energy of the disk is converted into kinetic energy as it rolls down the incline:
$mgh=\frac{1}{2}mv^2+\frac{1}{2}Iω^2$
where m is the mass of the disk, h is the vertical distance the disk has traveled, v is the speed of the disk, I is the moment of inertia of the disk about its center of mass, and ω is the angular speed of the disk.
We can simplify this equation using the fact that the disk is rolling without slipping:
$h=\frac{3}{5}d\sinθ$
$v=\frac{2}{5}\sqrt{2gh}$
$I=\frac{1}{2}mr^2$
where d is the horizontal distance the disk has traveled (3.00 m in this case) and r is the radius of the disk. Combining these equations, we get:
$v=\frac{2}{5}\sqrt{2gh}=\frac{2}{5}\sqrt{2g\frac{3}{5}d\sinθ}=\frac{2}{5}\sqrt{2g\frac{3}{5}(3.00	ext{ m})\sin(25.0°)}\approx4.07	ext{ m/s}$
Therefore, the answer is choice C.

Quiz 10: Rotational Motion