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Circular motion
A particle is moving in a circular path.
If the force on the particle would suddenly
vanish (string cut) in which direction would
the ball fly off?
Angus rotates a stone that is attached to
the end of a cord at constant speed
(counterclockwise).
a. Which way is the stone accelerating?
b. In which direction is the net force on the
stone?
c.
In which direction is the ball traveling
when it is right in front of him?
d. If he lets the stone go in c, in which
direction would it fly off?
e. What effect does the string’s tug have on
the stone?
A scientist is completely isolated in a box moving smoothly
through space in a straight line.
Another scientist is in a similar box spinning smoothly in
space.
Each scientist can have anything she needs to detect
motion.
Which scientist can detect her motion?
1. The first box
2. The spinning box
3. Both
4. Neither
See p 105
Circular Motion
A cat runs across the
floor from A to B to C
without changing its
speed. Can we say for
sure that a force has
acted on the cat at B?
B
A
a. Yes, there had to be a force on the cat at B
b. Not necessarily, as the cat’s speed has not changed
See p107
C
Circular Motion
• An object will not move, or it will stay at a constant
speed if there is no resultant force acting on it.
• When an object moves at a constant speed in a
circle its direction constantly changes, so there
must be a force acting inwards to stop it flying
away
• This force is called the centripetal force
• When this force is removed the object will fly off in
a straight line
An object
moving in a
circle requires
a centripetal
force acting
inwards
Centripetal Acceleration
• Remember that acceleration = change in velocity
• Velocity is a vector (speed in a given direction), so
acceleration occurs if speed or direction change
• An object turning has a changing direction, so even if its
speed is constant its velocity must be changing and it
must be accelerating
• The centipetal force causes centripetal acceleration
towards the centre of the circle
m
v
F
v
F m
What variables increase the force needed?
Imagine spinning a mass around your head
• As the mass of the object increases the
centripetal force you need to stop it flying off
increases
• As the speed of the object increases the
centripetal force you need to stop it flying off
increases
• But as the length of the string* increases the
force you need to stop it flying off decreases
* Radius of the circle
What provides the centipetal force?
• The force is obvious when there’s tension
through a string (or handle) as in the hammer
throw, but less obvious without one video
• For cars going around bends centripetal force
comes from friction between the tyres and the
road. Without friction a car will skid off in a
straight line
• How does banking on a racetrack help?
• What provides the centripetal force for satellites?
A centrifuge is used to separate heavy
things in suspension from lighter things,
such as blood cells from the plasma
• As the mass of the object increases the centripetal force
you need to stop it flying off increases
• So at a certain speed the centrifugal force will hold
lighter objects in the liquid but will not be strong enough
to stop the heavier ones from moving outwards to the
end of the test tube.
Circular motion
A particle is moving in a circular path.
If the force on the particle would suddenly
vanish (string cut) in which direction would
the ball fly off?
Angus rotates a stone that is attached to
the end of a cord at constant speed
(counterclockwise).
a. Which way is the stone accelerating?
b. In which direction is the net force on the
stone?
c.
In which direction is the ball traveling
when it is right in front of him?
d. If he lets the stone go in c, in which
direction would it fly off?
e. What effect does the string’s tug have on
the stone?
A scientist is completely isolated in a box moving smoothly
through space in a straight line.
Another scientist is in a similar box spinning smoothly in
space.
Each scientist can have anything she needs to detect
motion.
Which scientist can detect her motion?
1. The first box
2. The spinning box
3. Both
4. Neither
See p 105
Circular Motion
A cat runs across the
floor from A to B to C
without changing its
speed. Can we say for
sure that a force has
acted on the cat at B?
B
A
a. Yes, there had to be a force on the cat at B
b. Not necessarily, as the cat’s speed has not changed
See p107
C
Circular Motion
• An object will not move, or it will stay at a constant
speed if there is no resultant force acting on it.
• When an object moves at a constant speed in a
circle its direction constantly changes, so there
must be a force acting inwards to stop it flying
away
• This force is called the centripetal force
• When this force is removed the object will fly off in
a straight line
An object
moving in a
circle requires
a centripetal
force acting
inwards
Centripetal Acceleration
• Remember that acceleration = change in velocity
• Velocity is a vector (speed in a given direction), so
acceleration occurs if speed or direction change
• An object turning has a changing direction, so even if its
speed is constant its velocity must be changing and it
must be accelerating
• The centipetal force causes centripetal acceleration
towards the centre of the circle
m
v
F
v
F m
Uniform Circular Motion
An object rotating at steady speed
A
r
If the frequency = f
and period = T
What is the speed of A?
Angular Displacement and Angular Speed
Angular displacement θ is the angle in radians through
which an object has rotated in time t
θ = t/T x 2π = 2πft in rads
Angular speed
per second
ω (omega) is the angular displacement
ω = θ/t = 2π/T = 2πf
What is the unit?
r
ϴ
ω = 2π/T = 2πf
s
If length of the
arc = s
s = vt
= 2πr/T x t
= 2πrt/T
As θ = 2πt/T
s = θr
And the speed of rotation of the object
v = 2πr/T = ωr (see p23)
Centripetal force
Loop the Loop:
https://www.youtube.com/watch?v=wiZoVAZGgsw&feature=
youtube_gdata_player
See also Indian wall of Death
A rider in a “barrel of fun” finds
herself stuck with her back to the
wall. Which diagram correctly
shows the real forces acting on her?
The force depends upon;
•Mass
•Radius
•velocity
Centripetal force
F=m
r
a=
2
v
2
v
r
So what is the force on a
sock in a spin drier?
Note that the centripetal force
is proportional to the square
of the velocity, implying that a
doubling of speed will require
four times the centripetal
force to keep the motion in a
circle.
If the centripetal force must
be provided by friction alone
on a curve, an increase in
speed could lead to an
unexpected skid if friction is
insufficient.
Also, F =
2
m r
Jeff Gordon leads his race and must drive into a curve at top
speed to win it all.
a. What limits the speed at which he can negotiate the curve?
b. If he goes into a curve of 200 m radius with a speed of 100
m/s, what centripetal acceleration does he experience?
What is the acceleration of your room?
This is not an idle puzzle. Copernicus argued the earth orbits the sun.
On the other side Aristotle, Ptolemy and many others believed that
the sun must go around the earth, because they did not feel the
motion of the earth. Who is correct?
We do not feel constant velocity (try closing your eyes on a smooth
train or plane ride), but we do feel accelerations, both by the forces
on us that cause accelerations and by the forces acting in the middle
ear when the head accelerates.
So, what is your acceleration due to the rotation and orbital motion of
the Earth?
You will need to know some values: the period of the Earth's rotation
is (slightly less than) 24 hours. The actual value depends on your
latitude, but your distance from the Earth's axis is not greater than
six thousand kilometres. So What is the acceleration due to the
Earth's rotation about its axis?
To get an idea whether you would feel this, you could express your
answer as a fraction of g. You should do a similar calculation for the
acceleration due to the Earth's orbit, which has a radius of
1.5 x 1011 m.
London eye
A big wheel
Slow
Zodiac
Fast
lift
F
A banked turn
Bigger F