Question

A uniform disk rotating with constant angular acceleration covers 50 complete rotations in 50 secinds

Answer 1

Α = angular acceleration = rad/sec²t = time = 5 sec.ω₀ = initial angular velocity = 0 rad/sec as the body is at rest at t = 0 sec.θ = total angle rotated from t=0 to t, = 50 * 2π radians.Total angle rotated = θ = ω₀ t + 1/2 * α * t² (It`s like: total distance = s = u t + 1/2 * a * t²)So 100 π = 0 * 5 + 1/2 * α * 5² α = 8π rad/sec² = 8π /(2π) revolutions/sec² , as 1 revolution = 2π rad. = 4 revolutions/sec². α = 4 rev/sec.========================= direct calculation in rev/sec²Total angle rotated = θ = ω₀ t + 1/2 * α * t² 50 rev = 0 * 5 + 1/2 * α * 5² α = 4 rev/sec²