Posted by **Sam** on Tuesday, October 23, 2012 at 8:38am.

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.20x10^4 rad/s to an angular speed of 3.14x10^4 rad/s. In the process, the bit turns through 1.92x10^4 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 7.85x10^4 rad/s, starting from rest?

- Physics -
**Jennifer**, Tuesday, October 23, 2012 at 10:25am
w = w0 + a*t

theta = w0*t + 1/2*a*t^2

where w is the angular speed, w0 is the initial angular speed, and a is the angular acceleration, and theta is the angle turned in radians, so

3.14*10^4 = 1.2*10^4 + a *t

1.92*10^4 = 1.2*10^4*t + .5*a*t^2

Solve this system of equations using algebra for a and t

Then, use

7.85*10^4 = 1.2*10^4 + a*t,

where you know a from before, and you now solve for time

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