Question

A dentist's drill starts from rest. After 3.20 s of constant angular acceleration it turns at a rate of 3.00 ✕ 10⁴ rev/min.

(a) Find the drill's angular acceleration.
rad/s²
(b) Determine the angle (in radians) through which the drill rotates during this period.
rad

Answer 1

(A) Initial angular velocity of drill ( as it starts from rest ) " Wi " = 0 rev/s

final angular velocity ( Wf ) = 3.00 * 10^4 rev/min

now we know that ,

1 rev = (2 ) rad.

so ,

Wf = 3140 rad/s

we have time taken = 3.20 sec

therefore, ANGULAR ACCELERATION =:

  ^2

(B) now ,we know that drill undergose rotational motion about a fixed axis at a constant angular acceleration , so  

{ where is angle (in radians) through which drill rotates.

therfore ,

  

The angle (in radians) through which the drill rotates during this period IS 5024 rad.

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