# Physics (Rotational Kinetic Energy)

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Hello,

The question is: A solid ball rolls along the floor with a constant linear speed v. Find the fraction of its total kinetic energy that is in the form of rotational kinetic energy about the center of the ball.

Krot/Ktotal = ?

The answer I keep getting is 3/1, but the online homework system says "Your response differs from the correct answer by orders of magnitude.". I know the I for a solid sphere is I = 2/3 mr^2, but I'm still stuck.

Thank you for the help.

• Physics (Rotational Kinetic Energy) -

KE=1/2mv^2 + 1/2 *2/3 mr^2*w^2

but v=rw
so w^2=v^2/r^2
KE=1/2mv^2+1/3 mv^2 = 5/6mv^2

what fraction is rotational?

1/3/(5/6)=2/5 or .4 is rotational
check my math.

• Physics (Rotational Kinetic Energy) -

KE=1/2mv^2 + 1/2 *2/5 mr^2*w^2 ..not 2/3 mr^2*w^2 its solid sphere not a hollow sphere.

so the fraction would be 2/7 not 2/5 as the final answer. But bob's approach seems correct.

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