Kinetic Energy of a Rolling Ball on a Horizontal Plane

AI Thread Summary
The discussion focuses on calculating the kinetic energy of a uniform ball rolling on a horizontal plane while moving along a circular path. The translational kinetic energy is given by T1=(m v^2)/2, and the rotational kinetic energy is T2=(I w^2)/2, with I=2/5 m r^2 and w derived from the relationship w = v/r. The main question raised is how to incorporate the kinetic energy associated with the ball's motion along the circular path of radius R. It is suggested that the kinetic energy of the ball's rotation around the center of the circle may need to be considered. Overall, the discussion seeks clarity on the total kinetic energy calculation in this scenario.
ChuckNorris
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Homework Statement



Uniform ball or mass m and radius r rolls on a horizontal plane without sipping, at the same time moving along a circular path of radius R. Speed of the center of mass is constant and equals v. Find it's kinetic energy.

Homework Equations



I=2/5 m r^2

The Attempt at a Solution



KE of ball's translation T1=(m v^2)/2

KE of ball's rotation T2=(I w^2)/2 ( w - angular velocity, from w r = v => w= v/r)

My problem is with the ball moving along a circle of radius R. Where does it come into play?
Do i have to add the KE of ball rotation around the center of the circle?

Any help will be appreciated.
 
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The ball is also rotating about a vertical axis as it moves in the circle.
 
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