(Solved): The object shown in the figure below consists of a thin rod of length =22.9cm and mass m=1.20 ...

The object shown in the figure below consists of a thin rod of length $?=22.9\mathrm{cm}$ and mass $m=1.20\mathrm{kg}$ with a solid ball of diameter $d=10.0\mathrm{cm}$ and mass $M=2.00\mathrm{kg}$ attached to its top. The object is free to pivot about a frictionless axle through the bottom of the rod. The object is initially vertical and at rest when it starts to rotate clockwise. (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in J)? 3 (b) What is the angular speed (in rad/s) of the rod and ball? $\mathrm{rad}/\mathrm{s}$ (c) What is the linear speed (in $\mathrm{m}/\mathrm{s}$ ) of the center of mass of the ball? $\mathrm{m}/\mathrm{s}$ (d) How does it compare with the speed had the ball fallen freely through the same distance of $27.9\mathrm{cm}$ ? (Express your answer as a percentage of $v$ fall $v_{\text{swing }}\text{ is }{v}_{\text{fall }}\text{ by }\%\text{. }$