Question

An automobile tire with a radius of 0.30 m starts at rest and accelerates at a constant angular acceleration of 2.0 rad/s^2 for 7.0 s. What is the angular displacement of the tire?

A. 32 rad
B. 25 rad
C. 28 rad
D. 49 rad

Answer 1

The tire undergoes an angular displacement θ in time t according to

θ = θ₀ + ω₀ t + 1/2 α t ²

where

θ₀ = initial angular displacement

ω₀ = init. ang. velocity

α = ang. acceleration

Here we have θ₀ = 0 and ω₀, so after t = 7.0 s with acceleration α = 2.0 rad/s², the wheel will have been displaced

θ = 1/2 (2.0 rad/s²) (7.0 s)² = 49 rad

making the answer D.