Question

A wheel is rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after start. The angular acceleration of the wheel is

Please help! it's quite urgent.
Points -50

Answer 1

α = angular acceleration = rad/sec²
t = 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/sec²

Total angle rotated = θ = ω₀ t + 1/2 * α  * t²
    50 rev = 0 * 5 + 1/2 * α * 5²
    α = 4 rev/sec²

Answer 2

Given:
Angular displacement of the wheel = θ=50×2π=100π
Initial angular velocity of the wheel = ω0=0
After, t = 5 seconds
θ=ω0t+12αt2⇒100π=12×α× (5)2⇒100π=12×α× 25⇒α=8π rad/s2  or 4 rev/sω=ω0+2αt⇒ω=0+8π×5=40π rad/s⇒ω=20 rev/s