6.5.1 Understanding Rolling Motion

Question 1

Understanding Rolling Motion

Answer 1

• Rolling is a combination of translational and rotational motion. The translational speed of a rolling object is related to its rotational angular velocity by .
• The point at the bottom of a rolling object in contact with the ground or other surface is instantaneously at rest. The ground applies the force of static friction that moves the object.
• The total kinetic energy of a rolling object is the sum of its translational and rotational kinetic energies

Question 2

Consider a wheel rolling without slipping. Which of the following is not correct?

Answer 2

The velocity of the rotational component of motion w is equal to the velocity vector of translational motion, vCM

Question 3

Representing motion as a combination of translational motion of the center of mass and rotation about an axis through the center of mass requires restrictions on the axis. Which of the following is not one of these restrictions?

Answer 3

The axis must be an axis of symmetry.

Question 4

A hollow, cyclindrical shell with mass M and radius R rolls without slipping with speed vcm on a flat surface. Which of the following is correct?

Answer 4

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

Question 5

For an object that is rolling without slipping, which of the following statements is not correct?

Answer 5

The instantaneous axis of rotation is through the center of mass of the object.

Question 6

Which of the following equations is not normally used in analyzing or solving problems involving rolling motion?

Answer 6

x(t) = Acos(wt + theta)

Question 7

Consider the diagrams shown. Which of the following is correct?

Answer 7

• Wheel A illustrates pure translational motion.
• Wheel B illustrates pure rotational motion.
• Wheel C illustrates the vector sum of pure translational motion and pure rotational motion.

Question 8

A sphere of radius R and mass M rolls without slipping down a ramp of height h. Which of the following is correct?

Answer 8

If the mass of the sphere is doubled, then the kinetic energy will also double.

Question 9

Evaluate the following as true or false. The wheel of a rolling bicycle is an example of a rigid body with both translational and rotational motion. Translation speed v for a point at a distance r from the axis is related to the angular speed w by v = rw. The tangential acceleration (at) is related to r and w by at = rw^2

Answer 9

false

Question 10

Which of the following is incorrect?

Answer 10

The force of a static friction does the work that results in the acceleration of a bicycle.