Question

A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is ______.

Options

• 24 rad

• 48 rad

• 72 rad

• 96 rad

Answer 1

A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is 96 rad.

Explanation:

ω₀ = 0, ω = 24 rad/s, t = 8 s

using ω = ω₀ + αt

∴ α = `(ω - ω_0)/"t"  = 24/8` = 3 rad/s²

From the kinematics of rotating motion,

θ = `ω_0"t" + 1/2 alpha"t"^2`

= `0 + 1/2 xx 3 xx (8)^2`

= `(3xx64)/2`

= 96 rad.