Circular Motion and Simple Harmonic Motion

Simultaneous shadow projection of circular motion and bouncing weight on spring.

What It Shows

One of the simplest of periodic motions is uniform circular motion. By shadow projecting both uniform circular motion and oscillatory simple harmonic motion onto a screen, one can show that these two seemingly different kinds of motion are actually identical.

How It Works

A 8 cm diameter plastic ball mounted near the edge of a 46 cm diameter disk undergoes uniform circular motion. The disk, oriented vertically, is driven by a 57 RPM motor.1 A large iron weight (14.87 kg), suspended from a stiff spring, is the simple harmonic oscillator. The spring/weight combination has been carefully chosen so that its period of motion is almost identical to the motor.

circular motion

circular motion

The oscillating weight and rotating ball are positioned as shown. The audience view of the rotating disk is clearly uniform circular motion. The lighting on the disk is edge on, and so the shadow is that of the ball oscillating vertically. The shadow of the weight of course looks the same as the front view of it. The weight is raised from its equilibrium position and released at the appropriate time. The two shadows (of the weight and ball) oscillate vertically in unison—a striking demonstration of the relation between these two very different yet very similar motions.

circular motion

Setting It Up

The spring/weight combination is suspended from heavy duty lab clamps and rods (3/4" diam) on a lecture cart. The disk/motor sits on the same cart and the entire ensemble is positioned close to the projection screen so that the shadows are nice and sharp. A slide projector (with or without lens) on an AV cart sits on the opposite side of the lecture hall—the further away, the sharper the shadows. Move the carts to adjust the lighting so that the shadow of the rotating disk is just a vertical line on the screen.

Comments

Because the frequencies of the two systems are not perfectly identical, the shadows start to noticeably get out of phase with each other after a dozen or so oscillations. The demonstration can be stopped before that happens.

1 Bodine Electric Co type NS1-33R speed reducer motor (1725 RPM with 30:1 gear ratio). The disk is cut from 1/8" thick masonite.