Afan blade rotates with angular velocity given by ωz(t)= γ − β t2, where γ = 5.20 rad/s and β = 0.810 rad/s3 . calculate the angular acceleration as a function of time t in terms of β and γ.

Answer : The angular acceleration is

Solution : Given,

The given angular velocity equation is,

At t = 0,    

At t = t,      

Angular acceleration : It is defined as the rate of change of angular velocity with respect to time.

Formula used for angular acceleration :

where,

= angular acceleration

= angular velocity at time 't'

= angular velocity at time '0'

t = time

Now put all the given values in this formula, we get the angular acceleration.

Therefore, the angular acceleration is

(newtons first law)

conservation of momentum law states :

momentum before collision = momentum after collision

momentum p (kg-m/s)= mass * velocity

say moving car=1 000 kg, velocity = 10 m/s then p = 1 000*10= 10 000 kg-m/s

say still car = 2 000 kg, velocity = 0 m/s then p = 2 000* 0 = 0 kg-m/s

total momentum prior to collision = 10 000 + 0 = 10 000 kg-m/s

momentum after collision = 10 000 kg-m/s

mass now = 1 000 kg+2 000 kg = 3 000 kg

10 000 = 3 000 kg* velocity m/s

10 000/3 000 = velocity

3.33 m/s = velocity after collision

an impulse is a force applied over time , momentum is exclusive of external forces and a perfect collision is implied

c. 4.54 x 10–12 j happens to be correct