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# Rotational Quantities

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```									Rotational Quantities

Going in Circles
Rotation vs Revolution
 Rotation is to spin on an axis, like a wheel;
 Revolution is to travel in a circle around a
center point, like cars on a race track.
Forces which cause motion in a
circle (revolutions)
 If an object is moving in a circle there is a
centripetal force causing the curving.
 Centripetal means “center-seeking”
 There are no centrifugal forces!
Gravity
 In space, gravity is the force that causes the
Moon to orbit (revolve around) the Earth,
and the Earth to orbit the Sun.
 That makes it a centripetal force!
 Newton was the Physicist who first
described mathematically gravity.
Newton’s Law of Universal
Gravitation
 Every object in the universe attracts every
other object with a force directly
proportional to the product of their masses
and inversely proportional to the square of
the distance between their centers.
 Formula to follow:
An Inverse Square Law!

m1m2
F G 2
r
But Why?
 Newton didn’t say why, he just derived the
math.
 In the centuries to follow, many laws were
shown to be inverse square proportions.
 The reason has to do with a “flat” universe
and Euclidean geometry.
 Einstein changed all this, but we’ll stick
with Newton.
Forces that cause an object to
rotate
 Torques cause objects to spin on their axis.
 A torque is a force acting over a length.
 The length is called a lever arm.
 F1L1 = F2L2, as in a seesaw or mobile.
 Steering wheels, crowbars, and doorknob
placement are all uses of torque.
 The center of gravity is where all the weight
of an object appears to be.
Rotational Inertia
 Objects rotating tend to keep rotating.
 As linear inertia is related to mass,
rotational inertia is related to moment of
inertia.
 The moment of inertia (nothing to do with
time) is how an object’s mass is distributed
around an axis.
Keep on Rotating!
 The conservation of rotation, so to speak, is
called the conservation of angular
momentum.
 When an ice-skater spins slowly but then
pulls her arms in, she speeds up because of
conservation of angular momentum.
Precession
 Combining angular momentum and torque
(in very mathematical ways) produces a
precession.
 The slow turn around the vertical axis of the
suspended bicycle wheel.
 As the World Turns (ahem), the torque
produced by the Sun and Moon on our
planet causes the Earth to precess every
25,000 years.

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