Page 33 - Making things move_ DIY mechanisms for inventors, hobbyists, and artists

14 Making Things Move

Speed and Velocity

Speed is how fast something is moving. It’s measured in distance over time. Velocity
is the same thing, just in a specific direction. Common units are miles per hour (mph)
or feet per second (ft/s). If you tell someone to drive 60 mph north, you are actually
expressing a velocity. Rotational velocity (also called angular velocity) is exactly what
it sounds like: the speed of something spinning. This is commonly expressed in
revolutions per second (rps) or revolutions per minute (rpm) and distinguished from
straight-line velocity (v) by using the symbol ω (the Greek letter omega). Tangential
velocity describes the speed of a point on the edge of the circle, which at one split
second in time is moving tangentially to the circle. See Figure 1-15 to visualize this. In
the bicycle example, think of rotational velocity as the speed the rear wheel spins by
itself, and tangential velocity as the speed of the bike along the ground.

As an example, let’s say you ride a bicycle with a cog attached to the rear axle that
has an 8 in diameter, and your tire is 32 in across. Circumference is equal to π (or
3.14) multiplied by diameter, so the circumferences of the sprocket and wheel are
about 25 in and 100 in, respectively. This means that if you pedal at the rate of 1 rps,
a tooth on the sprocket travels 25 in per second, while a corresponding spot on the
wheel travels through 100 in. So the point on the wheel has a tangential velocity
four times higher than the sprocket, even though they have the same rotational
velocity of 1 rps. If the wheel shrunk down to the size of the sprocket, you would
need to pedal really fast to get anywhere (and look pretty funny doing it). So instead,
use the 1:4 mechanical disadvantage to help you cover more ground.

FIGURE 1-15 The rear sprocket on a bicycle wheel magnifies the speed of the wheel.