# Rotational inertia of a sphere

A bowler throws a bowling ball of radius R=0.11m along a lane. The ball slides on the lane with initial speed V of center of mass = 8.5 m/s and initial angular speed w = 0. The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic frictional force f acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed V of center of mass has decreased enough an angular speed w has increased enough, the ball stops sliding and then rolls smoothly.
A) What then is V center of mass in terms of w?

During the sliding, what are the ball's
B) linear acceleration and
C) angular acceleration?
D) how long does the ball slide?
E) how far does the ball slide?
F) what is the linear speed of the ball when smooth rolling begins?

The rotational inertia of a sphere is I = 2/5 mR^2.

What I have so far:

a) V center of mass = wR = 0.11w
b) f = -ma = umg, u = coefficient of kinetic friction.
a=-ug = -2.66m/s^2, negative because it's backwards. a here is linear acceleration.
c) torque = I*A = r x F, A = angular acceleration
2/5*(mR^2) A = rumg
A = (5/2R)*ug = 46.82 rad/s

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OlderDan
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chaose said:
A bowler throws a bowling ball of radius R=0.11m along a lane. The ball slides on the lane with initial speed V of center of mass = 8.5 m/s and initial angular speed w = 0. The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic frictional force f acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. When speed V of center of mass has decreased enough an angular speed w has increased enough, the ball stops sliding and then rolls smoothly.
A) What then is V center of mass in terms of w?

During the sliding, what are the ball's
B) linear acceleration and
C) angular acceleration?
D) how long does the ball slide?
E) how far does the ball slide?
F) what is the linear speed of the ball when smooth rolling begins?

The rotational inertia of a sphere is I = 2/5 mR^2.

What I have so far:

a) V center of mass = wR = 0.11w
b) f = -ma = umg, u = coefficient of kinetic friction.
a=-ug = -2.66m/s^2, negative because it's backwards. a here is linear acceleration.
c) torque = I*A = r x F, A = angular acceleration
2/5*(mR^2) A = rumg
A = (5/2R)*ug = 46.82 rad/s
If you have both accelerations correct, you can write the equations for velocities in terms of time. At some time the "final" velocities will correspond to rolling. The velocity values and the time are three unknowns, but you have three equations. They can be solved for the velocities and the time. D, E, and F are all related to these variables.

thanks. i didn't think of that