A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)=γt+βt3, where γ= 0.350 rad/s and β= 1.20×10^−2 rad/s^3.

a. Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in radians per second in terms of γ, β, and t. ω(t) = rad/sec
b. What is the initial value ω0 of the angular velocity? Express your answer in radians per second. ω0 = rad/s
c. Calculate the instantaneous value of the angular velocity ω(t) at time t=5.00s. Express your answer in radians per second. ω(5.00) = rad/s
d. Calculate the average angular velocity ωav for the time interval t=0 to t=5.00 seconds. Express your answer in radians per second. ωav = rad/s

Explanation:

a. Angular velocity, is defined as the rate of change of position of a rotating body with respect to time. so omega,= theta/time and theta =the position angle.

-Angular velocity of the merry-go-round can thus be calculated and  expressed as:

b. From a above, we know that our angular velocity is ,we can substitute to find our initial velocity.

Hence the value of angular velocity at t=0 is 0.350rad/s

c. To calculate the instantaneous angular velocity at t=5.00s, we

Therefore, the instanteneous angular velocity is 1.25rad/s

d. The average angular velocity between t=0 and 2=5s is calculated as

-At t=0,

-At time t=5s,

Therefore, the average angular velocity is calculated as

Hence the average angular velocity is 0.7rad/s

#instantenous angular velocity does not increase linearly .