Download Gravitation and Rotational Motion

Gravitation and Rotational Motion
Hannah Packer
Things to know:
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Kepler’s Laws
Newton’s Law of Universal Gravitation
Gravitational force
Gravitational constant
Gravitational Field
Angular Displacement
Angular Velocity
Angular Acceleration
Lever Arm
Torque
Center of Mass
Centrifugal Force
Key Concepts for Gravitation:
1. Kepler’s 1st Law- Path of the planets are ellipses, with the Sun at one
focus.
2. Kepler’s 2nd Law- An imaginary line from the sun to a planet sweeps
out equal areas in equal time areas.
3. Kepler’s 3rd LawT is equivalent to the period of a planet revolving around the Sun, and r
is the average distance from the sun.
Newton’s Law of Universal Gravitation: this says that objects attract
other objects with a force that is proportional to the product of their
masses and inversely proportional to the square of the distance
between them.
Other important equations include:
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Period of a Planet Orbiting the Sun – this is equal to 2 x pi times
the square root of the orbital radius cubed, divided by the
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product of the universal gravitational constant and the mass of
the sun.
Speed of a Satellite Orbiting Earth- this is equal to the square root
of the universal gravitational constant times the mass of Earth,
divided by the radius of the orbit.
Period of a Satellite Orbiting Earth- this is equal to 2 x pi times the
square root of the radius of the orbit cubed, divided by the
product of the universal gravitational constant and the mass of
Earth.
Gravitational Field- this is equal to the universal gravitational
constant times the object’s mass, divided by the square of the
distance from the object’s center.
Key Concepts for Rotational Motion:
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As an object rotates, the change in the angle is called
angular displacement. Counterclockwise rotation is
designated as positive while clockwise motion is negative.
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The angular velocity of an object is angular displacement
divided by the time taken to make the displacement.
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Angular acceleration is defined as the change in angular
velocity divided by the time required to make the change.
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For a given applied force, the change in angular velocity
depends on the lever arm, which is the perpendicular
distance from the axis of rotation to the point where the force
is exerted.
Torque- is a measure of how effectively a force causes rotation. The
magnitude of torque is the product of the force and the lever arm. Torque
is measured in Newton-meters.
p.s. (multiply by sin theta if used at an angle)
Newton’s Second Law for Rotational Motion: states that angular
acceleration is directly proportional to the net torque and inversely
proportional to the moment of inertia.
Center of Mass- this is the point on an object that moves in the same way
that a point particle would move.
Centrifugal Force- This is the apparent force that seems to pull on a
moving object, but does not exert a physical outward push on it, and is
observed only in rotating frames of reference.
Multiple Choice
If the radius of the Earth were increased by a factor of 2 and its mass
remained the same, then the acceleration due to gravity on the Earth
would…?
A) Increase by a factor of 4
B) Reduce by a factor of 4
C) Reduce by a factor of 2
D) Increase by a factor of 2
Free Response
Figure 1 shows an object with several forces acting on it. The pivot
point is at O.
F1 = 10 N, and is at a distance of 0.25 m from O, where = 80
F2 = 7.0 N, acting perpendicular to the object, at a distance of 1.25 m
from O
F3 = 12 N, is 0.60 m from O, and acts at
= 40 from the horizontal
Find the total (net) torque on the object.
Answers:
Multiple choice= Reduce by a factor of 4
Free Response= -6.6 N m