6.5.2 Solving Problems Involving Rolling Motion

Question 1

Solving Problems Involving Rolling Motion

Answer 1

• The principle of conservation of energy is very useful when solving problems involving rolling motion.
• The final speed of an object rolling down an inclined plane is . This is less than that of an object that slides down the plane without friction because some of the rolling object’s initial potential energy must be converted into rotational,rather than translational, kinetic energy.
• Objects with smaller moments of inertia reach a greater final speed at the bottom of the incline.

Question 2

Consider the case of a solid sphere, a solid cylinder, and a hoop (thin cylindrical shell) released from rest on an incline of height h. Assume the objects roll without slipping and that there is no energy loss due to friction. Which of the following is correct?

Answer 2

The potential energy of the objects is converted into translational and rotational kinetic energy.

Question 3

Consider a solid, rigid spherical ball released at the top of a hard-surfaced inclined plane. It rolls without slipping. Which of the following is incorrect?

Answer 3

The notation fs represents the force of static friction, which acts at the point of contact and it does work to oppose the motion of the ball rolling down the ramp.

Question 4

Which of the following is the equation for the total kinetic energy of a rigid body that is rolling without slipping?

Answer 4

K = 1/2Mvcm^2 + 1/2Icmw^2

Question 5

A bowling ball of mass M and radius R is released at the top of a hard-surface inclined plane. The plane makes an angle theta with the horizontal. The ball rolls with-out slipping with only static friction between it and the plane. Which of the following statements concerning the acceleration of the ball’s center of mass is correct?

Answer 5

The acceleration is 5/7 as large as it would be if the ball could slide without friction down the incline.

Question 6

A thin-walled, cylindrical ring with mass M and radius R rolls without slipping down an incline of height h with speed vcm. Which of the following is correct?

Answer 6

Half of the kinetic energy is translational and half is rotational.

Question 7

A uniform, cylindrical hoop of mass m is released from rest at the top of an inclined plane of height h. The cylinder rolls without slipping. Which of the following is not used to find the linear speed of the cylinder’s center of mass at the bottom of the incline?

Answer 7

Use mgh = 1/2Icmw^2 + 1/2mvcm^2 and solve for w^2 to determine w

Question 8

A car accelerates from rest at 3.2 m/s^2. The wheels have radii of 0.31m and roll without slipping. What is the final angular speed (w) of the wheels after the car has traveled 0.35 km?

Answer 8

1.5*10^2 rad/s

Question 9

A weight of mass m is attached to a rope that is wound around a wheel of radius r. The rope does not slip, no friction is present, and the weight is allowed to drop from rest. After the mass m drops a distance h, what is the kinetic energy of the wheel if the mass has velocity v ?

Answer 9

mgh - 1/2mv^2

Question 10

Which of the following statements about solving problems involving rolling motion is incorrect?

Answer 10

You often need to determine the linear speed of the center of mass of an object at the bottom of an incline of height h. In order to do this, you need to add the height of the incline to the distance to the object’s center of mass.