An automobile tire having a temperature of −1.6 ◦C (a cold tire on a cold day) is filled to a gauge pressure of 22 lb/in2 . What
1 answer:
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(a)
The angular acceleration of the pulley can be found by using the equivalent of Newton's second law for rotational motions:
(1)
where
is the net torque on the pulley
is the moment of inertia of the pulley
is the angular acceleration
First, we need to find the net torque. The torque exerted by the force F (forward) is:
While the frictional torque (backward) is . So, the net torque is
Now, re-arranging eq.(1), we find the angular acceleration:
(b)
Assuming that the string holding the bucket is inextensible, the bucket should have the same linear acceleration of a point on the edge of the pulley, which is given by
where
is the angular acceleration
r = 0.330 m is the radius of the pulley (the distance of a point at the edge from the centre)
Substituting into the equation, we find