Question

A solid body starts rotating about a stationary axis with an angular acceleration `alpha=alpha_(0) cos theta`, where `alpha_(0)` is a constant and `theta` is an angle of rotation from the initial position. Find the angular velocity of the body as a function of `theta`.

Answer 1

`alpha=alpha_(0) cos theta`
`omega(domega)/(d theta)=alpha_(0) cos theta`
`int_(0)^(omega)omegadomega=alpha_(0)int_(0)^(theta)costheta d theta`
`(omega^(2))/(2)=alpha_(0)sintheta`
` omega^(2)=2 alpha_(0)sintheta`
`omega=pmsqrt(2alpha_(0)sintheta)`