Download 3.1-3.2 Circular Motion - York Catholic District School Board

3.1-3.2 Circular Motion
Let’s take a look at your
diagram
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During your investigation, you might
have noticed a few things when you
released the stopper at various points
Is velocity constant when an
object moves in a circle?
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Can you keep an object moving at a
constant velocity when it moves in a
circle?
THE ANSWER IS YES AND NO
What aspect of velocity can you keep
constant?
What aspect of velocity changes?
Direction changes, speed is
constant
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Even though only one aspect of the
velocity vector changes, that still means
change
And a change in velocity means…
ACCELERATION
And where there is acceleration, there
is…
FORCE
Constant speed, changing
direction
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Circular motion can be seen as a large
number of straight velocity vectors
adding up to give you circular motion
Much like a circle itself can be made up
of a large number of small straight lines
The smaller those lines are, the closer
you get to a perfect circle
See the progression?
What forces do you feel?
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When you are spinning the mass, what
forces did you feel?
What keeps the mass from flying out of
the circle (which is what happens when
you let go…)
Centrifugal vs. Centripetal force
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You will notice that when the mass
spins, it pulls out of the circle
Think about what happens when you
spin a small child around by their arms –
what do you notice?
This force – the force that a spinning
mass seems to exert outwards – is
known as the CENTRIFUGAL FORCE
What keeps the mass from flying
away?
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If the mass pulls outwards during circular
motion, the one thing keeping it from
flying out MUST be an opposing force
inwards
In the case of your little experiment, what
was it?
Centripetal force
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In the case of your experiment, the tension
in the string provides what is known as a
CENTRIPETAL FORCE that pulls inward
This constant force “yanks” the mass
inwards, forcing the velocity vector to
constantly turn inwards
Therefore, if the force pulls inwards – so
does the acceleration it causes
Centripetal force is external to
the mass
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This could be string, a rod – anything that is
attached to the rotating mass that keeps it
from flying out of its rotational circle
Even gravity – planets move around the sun
at a constant speed in a circular motion
because the sun’s gravitational pull creates a
centripetal force that keeps us in orbit
If the planets did not maintain a constant
speed, what would we notice on earth?
Which one do we pay attention
to?
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Essentially, if an object is moving
uniformly in a circle, it means that the
centrifugal and centripetal forces are
balanced out
Most questions will ask you to find
centripetal force – and usually it is
assumed if we are dealing with uniform
motion that they are equal
Centrifugal force is described
via the the rotating mass
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Centrifugal force is a necessary “invisible” force used
to describe the path of objects moving in a circle
Since a rotating object is in a non-inertial frame of
reference that means that the forces the mass
experiences must be explained somehow
As you spun the mass faster, what did you notice?
The greater the speed of the object rotating, the larger
the centrifugal force, therefore requiring a larger
centripetal force to keep it in a circle
A false force
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Centrifugal force is a false force – it is
the force “felt” by an object due to its
inertia
The object wants to maintain its motion,
so it resists the centripetal force being
applied
This gives the impression of a “force”
being produced that opposes the
centripetal
Centripetal acceleration pulls inwards – but don’t
forget that the mass “pulls” outwards creating
the sensation of centrifugal acceleration
v1
Fcp
Fcf
v2
At an instant in the object’s path – notice that the
vector doesn’t change in its position either inwards
or outwards – rather, if released, will move
tangentially away – thus Fcp and Fcf are balanced
v1
Fcp
Fcf
The equations
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So how do we get the numbers?
The equation for centripetal acceleration
is determined by looking at the velocity
vectors at an instant and another
measureable quantity in the motion of
the circle – the radius