Calculating Tension and Acceleration in a Rotating System

[bard]

An object of mass m is tied to a light string wound around a wheel that has a moment of inertia I and radius R. The wheel bearing is frictionless and the string does not slip. find the tension and the acceleration of the object.

I think mg-T=ma


and that I=MR^2

thats all i know can someone help me please

thank you

 

[Doc Al]

You need to apply Newton's 2nd law to each body: the mass and the wheel.

Originally posted by bard
I think mg-T=ma

Right. That's Newton's 2nd law applied to the mass.

Now apply it to the wheel, using the rotational form: Torque = I*α (you tell me the torque).

To relate the two equations, note that a = R*α.

 

[bard]

Hi Doc Al,

Almost solved it
the a i use here will be angular acceleration

so

net torque=T*R or

Ia=T*R

Ia=(mg-mRa)R

Ia=mgr-mR^2a

Ia+mgR^2a=mgr
a(Ia+mR^2)=mgr

a=mgr/I+mR^2

for acceleration the tension is a=mR^2g/(I+mr^2)