Question

A disc rotates about axis its angular velocity w varries with time according to the equation w=at+b initially at t=0 angular velocity 1rad per second and angular position 2rad at t=2sec angular velocity 5rad per sec. Determine angular position and angular acceleration

Answer 1

$$w(0)=b=1\frac{rad}{s}$$

The angular acceleration:

$$a=\frac{5-1}{2-0}=2\frac{rad}{s^2}$$

The angular position:

$$\phi=0.5at^2+bt+c=t^2+t+c$$

$$\phi(0)=c=2\ rad$$

Thus,

$$\phi=t^2+t+2$$