Q. A stone is swinging in a horizontal circle 0.8 m in diameter, at 30rev/min. A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? What is the frequency?
A) 0.4 m, 1.5 Hz
B) 0.4 m, 0.5 Hz
C) 0.8 m, 0.5 Hz
D) 0.2 m, 0.5 Hz
Explanation
(b) The amplitude is the radius of the circle
$R = \frac{0.8}{2} = 0.4\ m$
The frequency of the shadow is the same as that of the circular motion, so
$\omega = 30\ rev/min\ \ $
$= 0.5rev/s = \pi\ {rads}^{- 1}$
$and\ \ \ v = \frac{\omega}{2\pi} = \frac{\pi}{2\pi} = 0.5\ Hz.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.