A solid sphere of mass $1.5\,\text{kg}$ and radius $15\,\text{cm}$ rolls without slipping down a $35^\circ$ incline that is $7\,\text{m}$ long. Assume it started from rest. The moment of inertia of a sphere is $I = \dfrac{2}{5}MR^2$.

Question

A solid sphere of mass $1.5\,\text{kg}$ and radius $15\,\text{cm}$ rolls without slipping down a $35^\circ$ incline that is $7\,\text{m}$ long. Assume it started from rest. The moment of inertia of a sphere is $I = \dfrac{2}{5}MR^2$.(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
, (b) Determine the angular speed of the sphere at the bottom of the incline.
, (c) Does the linear speed depend on the radius or mass of the sphere?
, (d) Does the angular speed depend on the radius or mass of the sphere?
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Rachel · Accepted Answer

$v \approx 7.5 \, \text{m/s}$
$\omega \approx 50 \, \text{rad/s}$
According to the equation derived in part (a) the speed does not depend on the radius or mass of sphere.
Angular speed does depend on the radius and does not depend on the mass of the sphere.

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