Download Uniform Circular Motion

Uniform Circular Motion
Uniform Circular Motion
Motion of an object moving in a circle at
constant speed.
 The linear velocity vector for an object in
uniform circular motion has a direction that
is constantly changing. Therefore, the
object experiences an acceleration.

Centripetal Acceleration (ac)

The acceleration experienced by an object
moving with uniform circular motion. It is
directed toward the center of the circular
path.
ac = vt 2 / r
or
ac = 4π2 r / T2
Ex: A car moves at a constant speed of
19.7 m/s around a circular track that
has a radius of 48.2 m. What is the
centripetal acceleration of the car?
Given: vt = 19.7 m/s
r = 48.2 m
Find: ac = ?
ac = v t 2 / r
= (19.7 m/s)2 / (48.2 m)
= 8.05 m/s2
Ex: A horse on a merry-go-round takes 13 s
to make one complete rotation. If the horse
is 6.0 m from the center, what is the
centripetal acceleration?
Given: T = 13 s
r = 6.0 m
Find: ac = ?
ac = 4π2 r / T2
= 4π2 (6.0 m) / (13 s)2
= 1.4 m/s2
Centripetal Force (Fc)
The force that maintains circular motion.
 The direction of Fc is toward the center of
the circular path.
 The centripetal force is not a special force.
Any force (friction, normal force, tension
force, gravity, etc.) can provide a
centripetal force.

Centripetal Force (Fc)
If ac is directed toward the center, and
∑ F = ma, then:
Fc = mac
Fc = mvt2 /r
Fc = m4π2 r / T2

Ex: A 70.5 kg pilot is flying in a horizontal
circle at a constant speed of 30.0 m/s. If the
circle has a radius of 100.0 m, what is the
centripetal force acting on the pilot?
Given: m = 70.5 kg
vt = 30.0 m/s
r = 100.0 m
Find: Fc = ?
Fc = mvt2 / r
= 70.5 kg (30.0 m/s)2 /100.0 m
= 634 N
Ex: A 65 kg person on a merry-go-round
takes 13 s to make one complete rotation. If
the person is 6.0 m from the center, what is
the centripetal force acting on her?
Given: m = 65 kg
T = 13 s
r = 6.0 m
Find: Fc = ?
Fc = m4π2 r / T2
= (65 kg) 4π2 (6.0 m)/(13 s)2
= 91 N