Rolling without Slipping

A sphere with mass 7kg and a diameter of 14cm is rolled down an inclined ramp, starting at rest, which makes an angle of 3 0 30^\circ with the horizontal. The incline has a height of 14m and has just enough friction so that the sphere rolls without slipping.

Remember that the moment of inertia for a sphere is 0.4m r 2 r^2 . Assume that g=9.8m/ s 2 s^2 . What is the linear speed (in m/s) of the sphere at the bottom of the incline? Submit your answer to 2 decimal places.


The answer is 14.00.

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1 solution

Sergio La Malfa
Apr 9, 2018

For Conservation of Energy

mgh=mgr+1/2mv²+1/2Iw²

I=2/5mr² and w=v/r

then mgh-mgr=7/10mv²

v²= g(h-r)10/7 v=14m/s

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