Question

A 60 cm diameter wheel accelerates from rest at a rate of 7 rad/s2. What is the tangential acceleration (in m/s2) of a point on the edge of the wheel?

Answer 1

Answer:

2.1 m/s²

Explanation:

By definition, the angular acceleration, is equal to the rate of change of the angular velocity, ω:

α = Δω / Δt (1)

By definition of the angular velocity, we can express the linear velocity, v, as follows:

v = ω*r⇒ Δv = Δω*r (2)

Replacing Δω, from (1) in (2), we get:

Δv = α*Δt*r⇒ Δv/Δt = α*r (3)

By definition of linear acceleration, we can write the following expression;

a = α*r

For a point on the edge of the wheel, the linear acceleration is tangent to the rim, and is equal to the product of the angular acceleration times the distance to the center, which for a point on the edge of the wheel, is just the radius:

⇒ a = 7 rad/sec²*0.3m = 2.1 m/s²