A Problem of my Book- 5
A semicircular ring is kept vertically on a horizontal surface as shown in the figure. The ring is in equilibrium initially. If the radius is . Find the time period in seconds of small oscillations of the ring. Assume that there is sufficient friction to prevent sliding.
The answer is 4.3.
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1 solution
We can solve it two ways 1)form the energy equation as a function of the angle that its vertical line rotates.now differentiate this eq and set it to zero as energy is conserved.(friction being sufficient to prevent slipping).2)we can assume some frictional force f and find the torque due to this force abt the centre of mass.this gives the angular acceleration of the object and relate it to the linear acceleration.