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Rotational motion problem help please

A mass (m) is connected to a pulley (rotational inertia I and radius R) which sits atop an incline with angle theta find an expression for angular acceleration in terms of M I R and theta.... incline is frictionless


using T= aI

i get Rmgsin(theta) = aI so a = Rmgsin(theta) over I

but alas this isnt correct and im not sure why

the correct answer has the same numerator but the denominator is I + mR^2 where is the mR^2 coming from? THANKS for any help
 

siddharth

Homework Helper
Gold Member
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Drawing the FBD of the mass, it is seen that the force acting down the plane is mgSin(Theta) and the force acting up the plane is Tension(T). From newton's second law,

mgSin(Theta)-T=ma.

and drawing the FBD of the pulley, The torque about the center of the pulley is due to the Tension of the rope only. So,

RT=I(alpha)

also,
a=R(alpha) [Can you see why this is so?]
From these three equations solve for alpha.
 

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