A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle.

(a) What is the speed of its center of mass when the disk reaches the position indicated by the dashed circle? (Use any variable or symbol stated above along with the following as necessary: g.)

Question

A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim (see figure below). The disk is released from rest in the position shown by the copper-colored circle.

(a) What is the speed of its center of mass when the disk reaches the position indicated by the dashed circle? (Use any variable or symbol stated above along with the following as necessary: g.)

anonymous · Answer

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anonymous · Answer

Since only internal conservative forces are acting, energy is conserved.
change in potential energy = gain in kinetic energy.$$mg \Delta h = 1/2 mv ^{2} + 1/2 I \omega ^{2}$$