Download Circular Motion

Circular Motion
Uniform Circular Motion


An object that moves
in a circle at a constant
speed, v.
The magnitude of the
velocity remains the
same but the direction
is changing so the
velocity changes
Acceleration

Acceleration is the change in velocity that
occurs over time. Since changing direction
changes the velocity the object moving in a
circle is constantly accelerating.
Centripetal acceleration

Centripetal Acceleration (center seeking)


Also known as radial acceleration aR (directed
along the radius of the circle)
aR = v2 /r



V is the linear speed,
R is the radius of the circle.
The direction of the acceleration is toward the
center of the circle.
Frequency and Period

Time Period, T
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Rotational Frequency, f


The time period of a circular motion is the time
taken for one revolution.
The rotational frequency of a circular motion is
the number of revolutions per unit time.
Thus the relation between time period and
frequency is T = 1/f


d = One revolution is 2 π r
v = d/t and t = T
So
v=2πr
T
Newton’s 2nd law (dynamics)

Σ FR = m aR = (mv2 )/r

Since the acceleration is directed toward the
center, and force and acceleration are in the same
direction, the force is also directed toward the
center.
Centrifugal force?



Not a real force.
Because 3rd law says forces must occur in pairs this
is a made up force that explains the outward force
that is felt when you go in a circle.
In order to move in a circle a force must be applied
to keep it in a circle. Otherwise the object will keep
going in the direction that it wants to go without that
force. THERE IS NO OUTWARD pushing FORCE
(no centrifugal force)
Sum of the forces

If working in the vertical direction or at an
angle, other forces must be considered as
well.
Maximum Speed on Banked
Roadway
Game Plan
1.
2.
3.
4.
5.
6.
Draw a free body diagram
Write down the givens
Write down what you don’t know and what you
need.
Resolve any forces that are at angles into the
components so that you are only dealing with x and
y forces.
Determine the magnitude of any known forces (e.g.
the force of gravity and label on the diagram
Use the circular motion equations to find the
unknowns.
examples
Sample Problem #1
 A 900-kg car moving at 10 m/s takes a turn around a circle
with a radius of 25.0 m. Determine the acceleration and the
net force acting upon the car.
 Known Information:



m = 900 kg v = 10.0 m/s
R = 25.0 m
Requested Information:a = ????
a = (v2)/R

Fnet = ????
a = ((10.0 m/s)2)/(25.0 m) = (100 m2/s2)/(25.0 m)
a = 4 m/s2

Fnet = m*a
Fnet = 3600 N
Fnet = (900 kg)*(4 m/s2)
more


Determine the centripetal force acting upon a
40-kg child who makes 10 revolutions around
the Cliffhanger in 29.3 seconds. The radius of
the barrel is 2.90 meters.
A 900-kg car makes a 180-degree turn with a
speed of 10.0 m/s. The radius of the circle
through which the car is turning is 25.0 m.
Determine the force of friction and the
coefficient of friction acting upon the car.
1.
A 1.5-kg bucket of water is tied by a rope and whirled in a circle with a
radius of 1.0 m. At the top of the circular loop, the speed of the bucket is
4.0 m/s. Determine the acceleration, the net force and the individual force
values when the bucket is at the top of the circular loop.
m = 1.5 kg
a = ________ m/s/s
Fnet = _________ N
2. A 1.5-kg bucket of water is tied by a rope and whirled in a circle with a
radius of 1.0 m. At the bottom of the circular loop, the speed of the bucket
is 6.0 m/s. Determine the acceleration, the net force and the individual
force values when the bucket is at the bottom of the circular loop.
m = 1.5 kg
a = ________ m/s/s
Fnet = _________ N