1. A dentist causes the bit of a high-speed drill to accelerate from an angular

Question

1. A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.05 104 rad/s to an angular speed of 3.14 104 rad/s. In the process, the bit turns through 2.12 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 7.85 104 rad/s, starting from rest?

a. A rotating object starts from rest at t = 0 s and has a constant angular acceleration. At a time of t = 7.0 s the object has an angular velocity of = 22 rad/s. What is its angular velocity at a time of t = 14 s?

Explanation / Answer

1. wi = 1.05 x 10^4 rad/s

wf = 3.14 x 10^4 rad/s

theta = 2.12 x 10^4 rad

Applying wf^2 - wi^2 = 2 alpha theta

putting values,

alpha = 2.06 x 10^4 rad/s^2

wf = wi + alpha t

7.85 x 10^4 = 0 + (2.06 x 10^4) t

t = 3.80 sec

(A) wf= wi + alpha t

22 = 0 + (alpha 7)

alpha = 22/7 rad/s^2

at t = 14 sec

wf = 0 + (22/7)(14) = 44 rad/s

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