Question

A high speed drill bit rotating counter clockwise at 1200 rpm slows to a stop in 3.0 seconds

A.) what is the drills angular acceleration in rad/sec^2?

B.)How many revolutions does the drill bit make before it stops?

Answer 1

Initial rotational speed of the drill bit = N₁ = 1200 rpm

Initial angular speed of the drill bit = ₁

₁ = 125.664 rad/s

Final angular speed of the drill bit = ₂ = 0 rad/s (Comes to a stop)

Time period = T = 3 sec

Angular acceleration of the drill bit =

₂ = ₁ + T

0 = 125.664 + (3)

= -41.89 rad/s²

Negative as it is deceleration.

Angle through which the drill bit rotates before stopping =

₂² = ₁² + 2

(0)² = (125.664)² + (2)(-41.89)

= 188.5 rad

Number of revolutions the drill bit makes before it stops = n

n = 30 rev

A) Angular acceleration of the drill = -41.89 rad/s²

B) Number of revolutions the drill bit makes before it stops = 30 rev