Question

A wheel at rest is rotated with a uniform angular acceleration, such that a particle on the rim of the wheel experiences a tangential acceleration of 20π ms–2. The radius of the wheel is 2 m. The instantaneous period of rotation at the end of 4 second is

Answer 1

Given info : A wheel at rest is rotated with a uniform angular acceleration, such that a particle on the rim of the wheel experiences a tangential acceleration of 20π ms–2. The radius of the wheel is 2 m.

To find : The instantaneous period of rotation at the end of 4 second is ....

solution : we know, angular acceleration, α = a/r

where a is tangential acceleration and r is radius.

⇒α = 20π/2 = 10π rad/s

as wheel starts from rest, ω₀ = 0

using formula, θ = ω₀t + 1/2 αt²

⇒θ = 0 + 1/2 × 10π × (4)² = 10π × 8 = 80π rad

therefore wheel rotates 80π rad at the end of 4 sec.