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Homework Statement
A thin light string is wrapped around a solid uniform disk of mass M and radius r, mounted as shown. The loose end of the string is attached to the axle of a solid uniform disc of mass m and the same radius r which can roll without slipping down an inclined plane that makes angle θ with the horizontal. Find the magnitude of the acceleration of the center of mass of the rolling disc, a. Neglect friction in the axles of the pulley and the rolling disk.
The Attempt at a Solution
1- I would use ##F=ma## for the disc and ##τ=Iα## for the pulley to write to equations and use the condition ##a=αr##.
2-friction b/w the incline causes torque in the disc
3-##I=0.5mr^2##
4-the net torque on the pulley will have a cos(θ) term (to have only perpendicular elements).
what I don't know-
will only the force of static friction cause net torque in the pulley (or T will cause torque in
the pulley)
edit:
assuming T causes torque
##Tr cos(θ)=0.5 M r^2 α##
##mgsin(θ)+μmgcos(θ)-T=m*a##
using ##α r= a##
I solved the equations but μ and cos(θ) terms don't get canceled
the answer is just in terms of M,m and g and θ
pleasez help!
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