Math Brush Up: Partial
Circumference
You can derive this
equation from the one for
taking the length of an arc.
Circumference of a circle
is equal to πr^2 ; a portion
of that (an arc) is found by
taking the angle of the arc
(θ) and using the equation
(θ/360)πr^2. After converting
to radians and treating
π as half a circle, you’ve
got the equation to find
the angular displacement
(one you solve for the
angle, θ).Therefore, the greater the value of r, or v = rω the greater the value of v. Points on
the rotating body farther from the rotation axis move faster than those closer to the
rotation axis.
From the equation v = rω, we can derive the relationship that connects angular
acceleration and linear acceleration.
a = rαIt’s important to realize that the acceleration a in this equation is not centripetal
acceleration, but rather tangential acceleration, which arises from a change in
speed caused by an angular acceleration. By contrast, centripetal acceleration does
not produce a change in speed. Often, tangential acceleration is written as at to
distinguish it from centripetal acceleration (ac).
- A rotating, rigid body makes one complete revolution in 2 s.
What is its average angular velocity?