Chapt. 12Rotational Dynamics11513. Dingo the daredevil dog is back—just accept it.He is now on a no-slip track and he curlshimself into an exactly spherically symmetric ball (but not necessarily a uniform density one)of radiusrDingo. Starting fromREST, he rolls down the track from an initial heighty0. Thetrack becomes level aty= 0, does a circular loop-the-loop of radiusR, and then goes level aty= 0 again. NoterDingoandRare different radii.a) What is Dingo’s center-of-mass speed at any heightyassuming he stays on the track?b) Find a general expression for the normal force on Dingo when he is on the loop as a functionof the angleθbetween a general radial vector and the radial vector pointing to the top ofthe loop and radiusR.c) For whatθis the normal force expression smallest? What is the normal force expressionfor this angle?d) What is the condition ony0/Rfor the normal forceNOTgo less than zero anywhere onthe loop? What happens if it did go less than zero?
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