Calculate the translational speed of a cylinder when it reac

Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.25 m high. Assume it starts from rest and rolls without slipping. Express your answer using three significant figures and include the appropriate units

Solution

By Conservation of energy

mgh =(1/2)mV²+(1/2)IW²

Since Moment of inertia of cylinder

I=(1/2)mr²

and W=V/r

=>mgh =(1/2)mV²+(1/2)[(1/2)mr²](V/r)²

mgh =(1/2)mV²+(1/4)mV²=(3/4)mV²

=>V=sqrt[(4/3)gh] =sqrt[4*9.8*7.25/3]

V=9.73 m/s