A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.20 104 rad/s to an angular speed of 3.14 104 rad/s. In the process, the bit turns through 1.92 104 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?

Question

A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.20  104 rad/s to an angular speed of 3.14  104 rad/s. In the process, the bit turns through 1.92  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?

Henry · Answer

3.14*10^4 - 1.2*10^4 = 1.94*10^4 rad/s. = Change in velocity. t=1.92*10^4rad * 1s/1.94*10^4rad=0.99s. T=7.85*10^4rad/s/1.94*10^4rad/s * 0.99s= 4.05 Seconds.