Question 6

A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by 'C'. The angular momentum from the origin O can be written as:

Solution

If the position vector from the origin makes an angle $$\theta$$ with the $$x$$-axis, the angle subtended at the center $$C(a, 0)$$ is $$2\theta$$ due to circle geometry.

The velocity $$\vec{v}$$ is tangential to the circle, and the perpendicular distance from the origin to this tangent is $$r_\perp = a + a \cos 2\theta$$.

$$L = mvr_\perp$$ (with $$m=1$$): $$L = va(1 + \cos 2\theta)$$

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A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by 'C'. The angular momentum from the origin O can be written as:

Solution

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