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

wavelength divides in half and speed stays the same.

conduction, convection, radiation