Download Uniform Circular Motion

Uniform Circular Motion
Acceleration
When an object moves at a constant speed
in a circular path, it is constantly changing
direction – accelerating
Δv
Centripetal Acceleration
Δv always points to the center of the circle
Since a = Δv/t, a must also be pointed to the
center of the circle
Centripetal Acceleration – center seeking
acceleration
Also called Radial Acceleration – directed
along the radius
Symbol - ar
Equation
a r = v2 / r
v is the velocity and r the radius
Greater v, faster direction changes, greater
the ar
Greater r, less rapidly changing direction,
lower the ar
v and a are always perpendicular to one
another at any given point on a circle
v
a
Frequency and Period
Circular motion is often described in terms
of frequency (f) and period (T)
Frequency – revolutions per sec – unit Hz
Period – time for one revolution – unit sec
The velocity is the distance traveled per
time
Distance is the circumference of the circle
which is 2π r
v = 2π r / T
Example 1
A 150 g ball at the end of a string is
revolving in a horizontal circle of radius
.600 m. The ball makes 2.00 revolutions in
a second. What is the centripetal
acceleration?
Example 2
The moon’s nearly circular orbit about the
earth has a radius of about 384000 km and a
period of 27.3 days. Determine the
acceleration of the moon toward the earth.
Force
Objects accelerating must have a force
acting on them therefore there must be a
force keeping an object in a circular path
This force is called Centripetal Force (Fr)
Fr = mar = mv2 / r
Since ar is directed into the center of the
circle, so is Fr
This force is always applied by other
objects
Factious Force
There is no force pulling objects out from
the center of a circle
There is an illusion of an outward force
caused by inertia
This factious force is called centrifugal
force
Example 3
What force must a person exert on a string
attached to a .150 kg ball in order to keep it
revolving in a horizontal circle of radius
.600 m ? The ball makes 2.00 revolutions
per second.
Example 4
In a tetherball game a .85 kg ball is hit in a
horizontal circle around a pole. The rope
makes an angle of 35° with the pole and is
holding the ball with a tension of 12.5 N.
The radius of its circular path is 1.25 m.
Find the centripetal acceleration, centripetal
force, the velocity, and period.