Chapter 11, Problem 75GP

A particle of mass m uniformly accelerates as counterclockwise along the circumference of a circle of radius R:

$\stackrel{\to }{r}=\hat{i}R\text{ cos }\theta +\hat{j}R\sin \theta$

with $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$, where the constants ${\omega }_0$and α are the initial angular velocity and angular acceleration, respectively. Determine the object’s tangential acceleration ${\stackrel{\to }{a}}_{tan}$and determine the torque acting on the object using (a) $\stackrel{\to }{\tau }=\stackrel{\to }{r}\times \stackrel{\to }{F}$, (b) $\stackrel{\to }{\tau }=I\stackrel{\to }{\alpha }$.