Question

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.46 x 104 rad/s to an angular speed of 3.29 x 104 rad/s. In the process, the bit turns through 3.02 x 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 9.56 x 104 rad/s, starting from rest?

Answer 1

Step 1:

Find angular acceleration of drill machine

Using 3rd rotational kinematic equation:

wf^2 = wi^2 + 2**

= angular displacement = 3.02*10^4 rad

wi = initial angular speed = 1.46*10^4 rad

wf = final angular speed = 3.29*10^4 rad

So,

= angular acceleration = (wf^2 - wi^2)/(2*)

= ((3.29*10^4)^2 - (1.46*10^4)^2)/(2*3.02&10^4)

= 14391.56 rad/sec^2

Step 2:

Now using above angular acceleration find time required to reach given angular speed

Using 1st kinematic equation:

wf = wi + *t

t = (wf - wi)/

Since in this case wi = 0 & wf = 9.56*10^4 rad/sec, So

t = (9.56*10^4 - 0)/(14391.56)

t = 6.64 sec

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