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2.

Problem 11.41P (HRW)

A wheel A of radius cm is coupled by belt B to wheel C of radius cm. Wheel A increases its angular speed from rest at a uniform rate of rad/s2 . We have to find the time for wheel C to reach a rotational speed of rev/min, assuming that belt does not slip.

Solution:             Click For PDF Version

Let at time t the angular speed of wheel A be and the angular speed of wheel C be . As the two wheels are connected by a belt which does not slip, the linear speeds at the rims of the two wheels has to be equal. This requirement gives the condition

Also, the angular acceleration of wheel A and the angular acceleration of wheel C will be similarly related, that is

We are given that

cm, cm, and = rad/s2. Therefore,

We will now calculate the time in which the wheel C will acquire the angular speed

As the wheel C is speeding up with constant acceleration the time in which it will attain this angular speed will be