Question

A flywheel turns through 30 rev as it slows from an angular speed of 5.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 15 of the 30 revolutions?

Answer 1

Initial angular speed of the flywheel = ₁ = 5.5 rad/s

Final angular speed of the flywheel = ₂ = 0 rad/s

Number of revolutions made by the flywheel before coming to rest = n = 30

Angle through which the flywheel rotates before coming to rest =

= 2n

= 2(30)

= 188.495 rad

Angular acceleration of the flywheel =

₂² = ₁² + 2

(0)² = (5.5)² + 2(188.495)

= -8.024 x 10^-2 rad/s²

Negative as it is deceleration.

Time taken by the flywheel to come to rest = T

₂ = ₁ + T

0 = 5.5 + (-8.024x10^-2)T

T = 68.54 sec

Time required to complete the first 15 revolutions = T₁

Angular displacement of the flywheel for 15 revolutions = ₁

₁ = 2(15)

₁ = 94.248 rad

₁ = ₁T₁ + T₁²/2

94.248 = (5.5)T₁ + (-8.024x10^-2)T₁²/2

(4.012x10^-2)T₁² - 5.5T₁ + 94.248 = 0

T₁ = 117.01 sec or 20.08 sec

T₁ cannot be greater than T (68.54 sec).

T₁ = 20.08 sec

a) Time taken by the flywheel to come to rest = 68.54 sec

b) Angular acceleration of the flywheel = -8.024 x 10^-2 rad/s²

c) Time taken by the flywheel to complete the first 15 of the 30 revolutions = 20.08 sec