Question

When a turntable rotating at 16 rev/min is shut off, it comes to rest in 26 s. Assume constant angular acceleration.

(a) Find the angular acceleration.
rad/s²

(b) Find the average angular velocity of the turntable.
rad/s

(c) Find the number of revolutions it makes before stopping.
rev

Answer 1

Initial rpm of the turntable = N = 16 rev/min

Initial angular velocity of the turntable = ₀

₀ = 2N/60

₀ = 2(16)/60

₀ = 1.6755 rad/s

Final angular velocity of the turntable = ₁ = 0 rad/s

Time taken by the turntable to come to rest = t = 26 sec

Angular acceleration of the turntable =

₁ = ₀ + t

0 = 1.6755 + (26)

= -0.0644 rad/s²

Negative as the it is deceleration.

Angular displacement of the turntable =

₁² = ₀² + 2

0² = (1.6755)² + 2(-0.0644)

= 21.79 radians

Number of revolutions made by the turntable before stopping = n

n = /(2)

n = 21.79/(2)

n = 3.47 revolutions

Average angular velocity =

Average angular velocity is equal to the angular displacement divided by the time period of the angular displacement.

= 0.838 rad/s

a) Angular acceleration = -0.0644 rad/s²

b) Average angular velocity = 0.838 rad/s

c) Number of revolutions made by the turntable before stopping = 3.47 revolutions