A flat mirror revolves at a constant angular velocity making...

A flat mirror revolves at a constant angular velocity making 2 revolutions/sec. With what velocity will a light spot move along a spherical screen with a radius of $10 \mathrm{~m}$, if the mirror is at a centre of curvature of the screen? (a) $251.2 \mathrm{~m} / \mathrm{s}$ (b) $261.2 \mathrm{~m} / \mathrm{s}$ (c) $271.2 \mathrm{~m} / \mathrm{s}$ (d) $241.2 \mathrm{~m} / \mathrm{s}$

A flat mirror revolves at a constant angular velocity making 2 revolutions/sec. With what velocity will a light spot move along a spherical screen with a radius of $10 \mathrm{~m}$, if the mirror is at a centre of curvature of the screen?
(a) $251.2 \mathrm{~m} / \mathrm{s}$
(b) $261.2 \mathrm{~m} / \mathrm{s}$
(c) $271.2 \mathrm{~m} / \mathrm{s}$
(d) $241.2 \mathrm{~m} / \mathrm{s}$

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Key Concepts

Angular Velocity

Angular velocity is the measure of how quickly an object rotates or revolves relative to a fixed point, expressed in radians per second. In many problems, including those involving circular motion, converting from revolutions per second to radians per second is essential because it allows the use of formulas that relate rotational motion to linear motion.

Law of Reflection and Angular Amplification

The law of reflection states that the angle of incidence equals the angle of reflection. When a flat mirror rotates, this law implies that the reflected beam rotates by twice the angle of the mirror’s rotation. This angular amplification is crucial in problems where a small change in the mirror's orientation produces a greater change in the direction of the reflected light, affecting the speed of the light spot on a screen.

Linear Speed on a Circular Path

Linear speed on a circular path is determined by the product of the angular velocity and the radius of the circle (v = ?R). This relationship connects rotational motion with linear motion, providing a method to calculate how fast a point on the circumference is moving, given its angular speed and the radius of the circle.

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