Find the angular acceleration and no. of revolution

Question

a rolling wheel, 60cm in diameter, starts from rest and accelerates uniformly and accelerates to a linear speed of 30m/s in 5sec. find the angular acceleration and b) the number of revolutions made in 6 sec.

Answer 1

When the linear speed is v, the angular speed is ω = v/(π*d) (radians per second).  The angular acceleration is α = ω/t, so α= v*/(π*d*t) (radian per sec²).  The angular distance covered is θ = 0.5*α*t² (radians), and the no of revolutions is θ/(2π).