Question

A wheel rotating with uniform acceleration covers 50 rev in the first five second after the start. Find the angular acceleration and the angular velocity at the end of five second.

Answer 1

At the end of five second,

Angular acceleration

α = 4 revolution/s²

angular velocity =

ω =20 revolution/s. 

◆Given,

Angular displacement, θ = 50 rev

time t = 5 sec.

◆Now , by equation of kinematics ,

θ = ωt +1/2 α t^2

◆By substitution,

50 = 0 + 1/2 α x 5² [ω=0 at rest]

25α = 100

α = 4 revolution/s².

◆After 5 second angular velocity will be ω'. then,

ω'=ω+ αt

◆Substituting values,

ω= 0 + 4 x 5

Angular velocity,

ω =20 revolution/s.