A car is driven in a flat circular curve of radius $r$ m. The car’s engine supplies a constant tangential driving force. The car experiences a friction heading towards the centre of the circle.
By writing $\ddot{\theta }$ as $\frac{d}{d\theta }\left ( \frac{1}{2}\dot{\theta }^{2} \right )$ find an expression for $\dot{\theta }^{2}$ in terms of $\theta$.
This is an easy question but I am just confused with the notation. Is $\dot{\theta }$ the rate of change of the angle? I know that the acceleration of the object tangentially is $a_{T}=r\ddot{\theta }=r\frac{d}{d\theta }\left ( \frac{1}{2}\dot{\theta }^{2} \right )$ but how will this help me answer the question?
Thank you!