An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is 8.2 times the magnitude of the tangential acceleration. What is the angle?

The angle is 4.1 rad.

Explanation:

The centripetal acceleration (α) is given by:

   (1)                  

Where:

ω: is the angular velocity  

r: is the radius

And the tangential acceleration (a) is:                      

     (2)

Since the magnitude of "α" is 8.2 times the magnitude of "a" (equating (2) and (1)) we have:

   (3)      

Now, we can find the angle with the following equation:

Where:

: is the final angular velocity                                                                              : is the initial angular velocity = 0 (it starts from rest)

: is the angle

    (4)    

By entering equation (3) into (4) we can calculate the angle:

Therefore, the angle is 4.1 rad.

I hope it helps you!                  

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