Question

A flywheel turns through 32 rev as it slows from an angular speed of 7.5 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 16 of the 32 revolutions?

Answer 1

Given Data

Initial angular velocity ω_o= 7.5 rad/s

Final angular velocity ω = 0.0 rad/s

Total angular displacement θ = 32 rev = 32 x 2π radian = 200.96 rad

Solution

A)

ω²= ω_o² + 2αθ

0²= 7.5² + 2α(200.96)

α = - 0.14 rad/s²

ω = ω_o + αt

0 = 7.5 + (-0.14)t

t = 53.59 s

B)

ω²= ω_o² + 2αθ

0²= 7.5² + 2α(200.96)

α = - 0.14 rad/s²

C)

Time taken for first 16 rev

θ₁ = ω_ot₁ + ½αt₁²

16 x 2π = 7.5t₁ + 0.5 x (-0.14)t₁²

100.48 = 7.5t₁ - 0.0699t₁²

0.0699t₁² - 7.5t₁ + 100.48 = 0

Solving the quadratic eqn, we get

t₁ = 15.7 s