When a bowling ball is thrown with an initial speed v, it is not spinning. After

Question

When a bowling ball is thrown with an initial speed v, it is not spinning. After a short time, friction will
cause it to roll without slipping. At that point, how fast will it be moving? I have given you the answer in
a previous homework, so the answer is insufficient in this case.

5) When a bowling ball is thrown with an initial speed v, it is not spinning. After a short time, friction will cause it to roll without slipping. At that point, how fast will it be moving?1 have given you the answer in a previous homework, so the answer is insufficient in this case.

Explanation / Answer

Initially the ball is not spinning so ball has only translational energy i.e. 1/2mv^2

But when friction cause it to roll it wil have translational plus rotational energy so total energy wil be 1/2mv^2+1/2Iw^2

For a ball moment of inertia is 2/5MR^2

w=v/R

So 1/2Iw^2=1/2 × 2/5MR^2 × v^2/R^2

=1/2 (2/5Mv^2)=2/5 (1/2Mv^2)=2/5(1/2Mv^2)

So total energy 1/2Mv^2+2/5 (1/2mv^2)=7/5×1/2Mv^2

So ball Has extra energy due to rotational motion

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