Question

a wheel is making revolutions about its axis with uniform angular acc .starting from rest it reaches 100 rev/sec in 4 sec find the angular acc find the angle rotated during these 4 sec

Answer 1

u = 0
v = 100 rev/s = 200*pi rad/s = 628 rad/s
t = 4s
angular acceleration, a = (628-0)/4 = 157 rad/s^2
angle rotated = (v^2 - u^2)/2a = (628^2)/2*157 = 1256 rad

Answer 2

ω1 = initial angular velocity = 0  rad/sec
ω2 = final angular velocity
     = 100 rev /sec * 2π radians/revolution
     = 200 π radians/sec
time duration = 4sec

angular acceleration α = (ω2 - ω1) / t  = 50 π  rad/sec²

angle rotated in time t = 0 to 4sec :
       Ф = ω1 t + 1/2 α t²  =  0 + 1/2 * 50π * 4² = 400 π radians.
           = 200 revolutions.