Engr Help

Principle of Work/Energy Plane Motion

Example: Bar, cde, of length R is fastened to a ring of radius R as shown below where d denotes

the center of mass of the bar and c denotes the center of mass of the ring. Both the bar and ring

are of mass m. The bar-ring assembly is initially at rest when it starts to roll down the incline, at

angle β, with an angular speed, ω. Determine the angular speed of the assembly, ω, after it travels

one revolution down the incline.

Strategy: Apply the principle of work and energy to the bar/ring system. W_1-2= T₂ ˗ T₁

where the subscript 1 denotes the initial position and subscript 2 the final position after one

revolution.

Solution: T₁ = 0 since system starts from rest. Click here for the calculation of T₂.

The work done is due to that for the bar and that for the ring. The figure below shows the

forces of gravity acting on the bar and on the ring.