A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 2.0 cm and accelerates at the rate of 6.6 rad/sec^2, and it is in contact with the pottery wheel (radius 25.0 cm) without slipping. (a) Calculate the angular acceleration of the pottery wheel. rad/sec^2 (b) Calculate the time it takes the pottery wheel to reach its required speed of 50 rpm.
Question
A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 2.0 cm and accelerates at the rate of 6.6 rad/sec^2, and it is in contact with the pottery wheel (radius 25.0 cm) without slipping. (a) Calculate the angular acceleration of the pottery wheel. rad/sec^2 (b) Calculate the time it takes the pottery wheel to reach its required speed of 50 rpm.
Solution
(a) The small wheel is in contact with the pottery wheel without slipping. This means the linear acceleration of the small wheel is equal to the linear acceleration of the pottery wheel.
We can calculate the linear acceleration of the small wheel using the formula:
Linear acceleration = Angular acceleration * Radius
So, for the small wheel:
Linear acceleration = 6.6 rad/sec^2 * 0.02 m = 0.132 m/sec^2
Since the linear accelerations are equal:
Angular acceleration of pottery wheel = Linear acceleration / Radius of pottery wheel
Angular acceleration of pottery wheel = 0.132 m/sec^2 / 0.25 m = 0.528 rad/sec^2
(b) We need to convert the required speed of the pottery wheel from rpm to rad/sec.
1 rpm = 2π rad/60 sec
So, 50 rpm = 50 * 2π rad/60 sec = 5.23599 rad/sec
We can use the formula for time in terms of angular acceleration and angular speed:
Time = Angular speed / Angular acceleration
Time = 5.23599 rad/sec / 0.528 rad/sec^2 = 9.92 sec
So, it takes approximately 9.92 seconds for the pottery wheel to reach its required speed of 50 rpm.
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