Rotational Kinetic Energy?

Question

A homogeneous solid cylinder rolls without slipping on a horizontal surface. The total kinetic energy is K. The kinetic energy due to rotation about its center of mass is...

Answer 1

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Total KE = KE(linear) + KE(rotational) 

K = ½mv² + ½Iω²

For solid cylinder, with axis along the length, I = ½mr²

Also we know ω = v/r

K = ½mv² + ½(½mr²)(v/r)²

K = ½mv² + ¼mv²

K = ¾mv²  ............(1)

KE(rotational) = ¼mv² ....(2)

(2) divided by (1) gives

KE(rotational)/K = (¼mv²)/¾mv²

KE(rotational)/K = 

from (1)

KE(rotational)/K = ⅓

KE(rotational) = ⅓ K

Answer (b)