Posted by Sam on .
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?
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
7.85*10^4 = 1.2*10^4 + a*t,
where you know a from before, and you now solve for time