1. A dentist causes the bit of a high-speed drill to accelerate from an angular
ID: 1605938 • Letter: 1
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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