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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!

Sigma
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  • Yes, $\dot{\theta}$ has units change in angle per time. Is this all the information you were given in the question? – Kris Williams May 19 '13 at 13:09
  • The question has 3 parts, this is part (a) so for this question, yes, this is all the information. – Sigma May 19 '13 at 13:12
  • Given the oddness of the second sentence ("The car experiences a friction..."), I suspect that the OP has left out some crucial information here. Are we told what this friction is, for example? – TonyK May 19 '13 at 13:58
  • Yes, sorry, I added the missing information. "The car’s engine supplies a constant tangential driving force" – Sigma May 19 '13 at 14:03

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