uniform circular motion - linville ucm.pdf · uniform circular motion • uniform circular motion...
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• Uniform circular
motion is motion
in a circle at the
same speed
• Speed is
constant, velocity
direction
changes
• the speed of an object moving in a circle is given
by
2 r
Tv
circumference
time
r= radius of circle
T = period, time for 1 complete
circle
Moon setting
over Rio de
Janerio
Pictures every
6.5 minutes
showing the
moon is moving
at a uniform
speed
• Since the velocity is changing direction, there is
an acceleration
• the centripetal acceleration of the object is
r
2vc
a
ac = centripetal acceleration
(always to centre of circle)
•the velocity vector is
always directed along the
tangent of the circle (at
right angles to the
acceleration vector)
•centripetal means centre-
seeking, the acceleration
vector always points to
the centre of the circle
Centripetal Force
• inertia tends to keep objects moving in a
straight line, a force is needed to cause a
circular motion (2nd Law of Motion)
• the force causing the motion is called the
centripetal force and it always acts
towards the centre of the circle (parallel to
the acceleration vector)
• an object will
move in a circle
whenever a
constant
magnitude force
acts on the object
at right angles
to its direction
of motion
• The string pulls ball
towards the centre of
the circle
• 3rd Law of Motion: a
reaction force will act
outward (ball pulls
string)
• this is sometimes
called centrifugal force
Important!!!
• centripetal force is not a fundamental force
like gravity, it is the net force acting on an
object moving in a curved path
• The force will not change the speed of the
object because the force has NO
component parallel to the velocity
vector
Practice
• A centrifuge for
pilot training is 11
m in radius. At
what speed must it
rotate in order to
inflict 7.0g of
acceleration on a
pilot?
Frequency of rotation
• sometimes speed is given in revolutions per minute (rpm) or revolutions per second (rps)
• this is how many times the object goes around the circle in 1 minute or 1 second
• frequency is the number of cycles per second measured in hertz (Hz)
Example
• Find the period of an object that rotates at 35.0
rps.
T
circle
s
circles 1
1
0.35
sT 0286.0
Free Body Diagrams
• A tetherball is attached to a
swivel in the ceiling by a light
cord. When the ball is hit by a
paddle, it swings in a horizontal
circle with constant speed, and
the cord makes a constant
angle with the vertical
direction. Write the expression
for the centripetal force in
terms of the other forces.
Free Body Diagrams
• An object is on a horizontal disc that is
rotating at constant speed. Friction
prevents the rock from sliding. Write the
expression for the centripetal force in
terms of the other forces.
•
Example
• A 3.50 kg object is swung in a 1.50 m radius
horizontal circle at 40.0 rps (40.0 Hz). What
magnitude force acts on the object?
2
2
4 mF m a F net c
T
r
Solution #2
2
2
4 mF m a F net c
T
r
N 510 x 3.32cF
s) (0.0250
kg) 3.50m) (1.504cF
r4cF
2
(2
2
2
T
m
224F so 1
rmfT
f
Effect of radius on speed and forces
• all points on a rotating
solid have the same
period, but different
speeds
• because the inner points
have smaller distances to
travel, their speeds are
less
• the speed and force
depends on the radius
• NASA and other space agencies use this to help launch satellites
• at the equator, the speed is about 1667 km/h, at Edmonton, it is about 900 km/h
Practice
• A 1100 kg car is moving
in a circle at 15.0 m/s. It
takes the car 12.5 s to
move from position 1 to
position 2. What is the
centripetal acceleration
of the car?
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