Question

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.35 x 10^4 rad/s to an angular speed of 3.90 x 10^4 rad/s. In the process, the bit turns through 2.55 x 10^4 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 7.43 x 10^4 rad/s, starting from rest?

Answer 1

Solution :-

Initial angular speed, w = 1.35 x 10^4 rad/s

Final angular speed, w' = 3.9 x 10^4 rad/s

Angular displacement, theta = 2.55 x 10^4 rad

Angular acceleration, a = [ w' ^2 - w ^2 ] / ( 2 * theta )

= 2.625x 10^4 rad/s^2

Case II:

w = 0 rad/s

w' = 7.43 x 10^4 rad/s

Time, t = ?

We have,

w' = w + a t

w' = a t

t = w' / a

= 7.43 x 10^4 / 2.625 x 10^4

= 2.83 s