Question

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.67 x 10⁴ rad/s to an angular speed of 4.55 x 10⁴ rad/s. In the process, the bit turns through 3.10 x 10⁴ rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 9.71 x 10⁴ rad/s, starting from rest?

Answer 1

here,

the initial angular speed , w0 = 1.67 * 10^4 rad/s

final angular speed , w = 4.55 * 10^4 rad/s

theta = 3.1 * 10^4 rad

let the angular accelration be alpha

using third equation of motion

w^2 - w0^2 = 2 * alpha * theta

(4.55 * 10^4)^2 - ( 1.67 * 10^4)^2 = 2 * alpha * ( 3.1 * 10^4)

solving for alpha

alpha = 2.89 * 10^4 rad/s

let the time taken be t for final speed , w' = 9.71 * 10^4 rad/s

w' = 0 + alpha * t

9.71 * 10^4 = 0 + 2.89 * 10^4 * t

solving for t

t = 3.36 s

the time taken is 3.36 s