9.6. Rolling Objects http://www.ck12.org
b. Determine the acceleration of the center of mass of the cylinder while it is rolling down the inclined
plane.
c. Determine the minimum coefficient of friction between the cylinder and the inclined plane that is re-
quired for the cylinder to roll without slipping.
d. The coefficient of frictionμis now made less than the value determined in part d so that the cylinder
both rotates and slips. How does the translational speed change from above (i.e. larger, smaller, same).
Justify your answer.- For a ball rolling without slipping with a radius of 0.10 m, a moment of inertia of 25.0 kgm^2 , and a linear
velocity of 10.0 m/s calculate the following:
a. The angular velocity.
b. The rotational kinetic energy.
c. The angular momentum.
d. The torque needed to double its linear velocity in 0.2 sec.
Solutions- a = 2gsinθ/3 b. (tanθ) /3 c. The translational, or linear speed increases because some of the energy that would
have gone into rotational kinetic energy now goes to linear kinetic energy, hence making the linear speed
greater. - a. 100 rad/s b. 1. 25 × 105 J c. 2500 Js d. 12,500 Nm