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Conservation of Energy in Rolling Motion

13. Rotational Inertia & Energy / Conservation of Energy in Rolling Motion / Problem 6

A composite object is made up of two solid cylindrical disks connected by a light rod of negligible mass, and it starts from a position of rest. The smaller disk has a mass of 0.025 kg and a radius of 0.05 m, while the larger disk has a mass of 0.15 kg and a radius of 0.10 m. This setup is arranged to rotate around the common axis of the cylinders and is dropped from a height of 2.0 meters without any initial rotation, in a situation where air resistance is ignored.
(a) Use the principle of conservation of energy to calculate the linear speed of the system just before it hits the ground.
(b) What fraction of its kinetic energy would be rotational just before impact?

A

$v_{cm} = 2.5 m / s, \frac{K_{r o t a t i o n a l}}{K_{t o t a l}} = 29 %$

B

$v_{\operatorname{cm}}=3.0m/s,\frac{K_{rotational}}{K_{total}}=78\%$

C

$v_{c m}=4.9 \mathrm{~m} / \mathrm{s}, \frac{K_{\text {rotational }}}{K_{\text {total }}}=75 \%$

D

$v_{c m}=5.1 \mathrm{~m} / \mathrm{s}, \frac{K_{\text {rotational }}}{K_{\text {total }}}=45 \%$

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