Now consider a fixed object spinning, like a compact disc. The relevant variables become the following:
These variables are related via the following three equations. Obviously, these equations differ from the
“star equations” used for kinematics ... but they’re nonetheless very similar:
So try this example:
A bicycle has wheels with radius 50 cm. The bike starts from rest, and the wheels speed up uniformly
to 200 revolutions per minute in 10 seconds. How far does the bike go?In any linear kinematics problem the units should be in meters and seconds; in rotational kinematics, the
units MUST be in RADIANS and seconds. So convert revolutions per minute to radians per second. To
do so, recall that there are 2π radians in every revolution:
200 rev/min × 2π rad/rev × 1 min/60 s = 21 rad/s.Now identify variables in a chart:
We want to solve for Δθ because if we know the angle through which the wheel turns, we can figure out
how far the edge of the wheel has gone. We know we can solve for Δθ , because we have three of the five