- #1
kidsmoker
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Homework Statement
I'm just working through a few past mechanics papers and this question came up:
A belt drives the circumference of a cylindrical wheel of radius R and mass M with
no slipping. The tension in the belt is T. Friction in the wheel bearing causes an
effective torque N to act on the wheel.
(i) If the velocity of the belt is constant, what is T in terms of N.
(ii) The bearing is lubricated removing all significant friction and the velocity of
the belt then increases with a uniform acceleration a. Write down T in terms of
M, R, and a.
I'd be greatful if someone could just check through my solutions so that I'm sure doing things correctly.
Homework Equations
I=0.5mR^2 for disc
v=wr
L=I(dw/dt)
The Attempt at a Solution
(i) T=N .
(ii) v=wR implies dw/dt = a/R .
Therefore TR = 0.5MR^2 * (a/R) ,
and so T = 0.5Ma .
Thanks.