Adentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.10 104 rad/s to an angular speed of 3.14 104 rad/s. in the process, the bit turns through 2.00 104 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?

3.63 s

Explanation:

We can solve the problem by using the equivalent SUVAT equations for the angular motion.

To find the angular acceleration, we can use the following equation:

where

is the final angular speed

is the initial angular speed

is the angular distance covered

is the angular acceleration

Re-arranging the formula, we can find :

Now we want to know the time the bit takes starting from rest to reach a speed of . So, we can use the following equation:

where:

is the angular acceleration

is the final speed

is the initial speed

t is the time

Re-arranging the equation, we can find the time:

For constant angular acceleration we can use

here we will have

now from above equation

now again by kinematics equation