A uniform 25 cm long stick rotates freely about a horizontal axis through one of its ends. It is released at an angle ? to the vertical. When it hangs straight down, the speed of the tip of the stick is 3 m/s. How large is ??

Asked by Jerrin Thomas | 24th Nov, 2013, 11:14: AM

Expert Answer:

The figure below represents the rotation of stick.

The centre of mass was at point B when the stick is held at an angle θ. When it hangs vertically down, it is at a distance BC' from the original position.

Now, from the triangle OAB, we have

CO = (L/2) cosθ.

Thus, the centre of mass has fallen through a distance BC' = (L/2)(1 + cosθ)

Now, the decrease in potential energy is

Mgh = Mg (L/2)(1 + cosθ)

This decrease in potential energy goes in increasing the kinetic energy.

Mg (L/2)(1 + cosθ) = ½ Iω2

Now, the moment of inertia of the stick about an axis through its end is

I = (1/3)ML2

Thus, we have

Answered by Romal Bhansali | 5th Dec, 2013, 12:46: PM

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