Transcript Uniform Circular Motion

Uniform Circular Motion
Basic Principles & Formulas
Uniform Circular Motion Principles
Object moving at a constant speed
(scalar)
Object’s velocity is constantly changing
due to a continuous change in direction
Velocity is tangent is to circular motion
While in motion, there is a force and an
acceleration being applied to the object
Uniform Circular Motion Questions
While moving in a circular path, if string
breaks, in what direction will the object
travel?
In a straight line, perp. to radius
(Law of Inertia)
In what direction is the force?
Inward
In what direction is the acceleration?
Inward
Uniform Circular Motion Diagram
Acceleration & Force = Parallel to Radius / Velocity = Perpendicular to Radius
v
a
r
f
Uniform Circular Motion Terms &
Formulas
Period (T) = time it takes to make 1
revolution
Period may be given, obvious or
determined by time/revolutions ex. 25 rev.
in 10 sec. T = 10/25  .4 sec (T = 1/f)
Frequency (f) = number of revolutions
made in 1 sec. (f = 1/T) units = Hz
Uniform Circular Motion Terms &
Formulas
Velocity (v) =
Acceleration (a) =
or
2πr
T
4π²r
T²
v²
r
Uniform Circular Motion Terms &
Formulas
Force (F) =
or
mv²
r
m 4π²r
T²
UCM Example Problem
A 615 kg race car completes 1 lap in 14.3
sec around a circular track with a radius of
50.0 m. What is the car’s T, f, v, a, F (on
tires)?
 T = 14.3/1
= 14.3
f = 1/14.3
= 0.07 Hz
UCM Example Problem (cont.)
V = (2)(π)(50.0)
14.3
= 21.97 m/s
a = (21.97 m/s)²
50.0
= 9.65 m/s²
UCM Example Problem (cont.)
F (on tires) = (615 kg)(21.97 m/s)²
50.0 m
= 5,936 N