Question:

Straight Forward Kinetic Energy and Angular Momentum Problem?

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A solid 1.0 kg ball of radius 0.50 m sits at the top of a ramp. It rolls down, ending up 10.0 m lower than where it started.

1) What is the TOTAL kinetic energy of the ball at the bottom?

2) How fast is the ball moving at the bottom of the ramp?

3) What is the ball's angular velocity and angular momentum at the bottom?

Now assume there is no friction. How would this change the above answers?

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  1. 1) The acceleration is 10m/s^2 give or take so the force on the ball is 10kg-m/s^2. This forced applied over 10m is 100kg-m^2/s^2 which is 100Joules.

    Its been awhile since I did kinematics problems and I'm a little busy at the moment so I can't refresh myself, but to the last portion I know that if there was no friction the ball would have the same KE but no angular velocity and thus it would be going faster at the bottom because the KE wouldn't be divided up between velocity and angular velocity.

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