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A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that...

A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 25° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? rad/s

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Answer #1

from energy coservation

[ rotational kinetic energy + translational energy + potentional energy ]top =[ rotational kinetic energy + translational energy + potentional energy ]bottom

at top

rotational kinetic energy = 0 since at rest on top

translational energy = 0   

and potentional energy =  

at bottom

rotational kinetic energy =

translational energy =

potentional energy = 0;

since no slipping

and

so from energy conservation :

so here we take g = 9.81 m/s^2

m/s

so angular velocity from  

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