Phys1111

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Phys1111

• Chapter 8
• Circular Motion, Central Forces, and Gravitation

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Circular Motion

• Uniform circular motion
• a body in uniform circular motion moves in a
  circle with constant speed
• The velocity of the body is always tangent to the
  circle
• Velocity is not constant because of the change in
  direction

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Circular Motion
In uniform circular motion, both the total force
on an object and the objects acceleration must
be perpendicular to the velocity and toward the
center of the circle.
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Circular Motion
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Circular Motion

• Example 1
• A large marry-go-round completes one revolution
  every 10.0s. A child of mass 20.0kg is sitting
  6.00m from the center.
• Compute the acceleration of the child.
• What centripetal force is acting on the child?

Additional Examples Example 8-1, Example 8-2,
Example 8-3
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The universal law of gravitation
Every particle attracts any other particle with a
gravitational force whose magnitude is given by
m2
m1
r
This equation is called Newtons universal law of
gravitation.
Here m1 and m2 are the masses of the two
particles, r is the distance between them, and G
is the universal gravitational constant. G
6.67x10-11N.m2/kg2
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The universal law of gravitation

• Example 2
• Two objects exert a gravitational force of
  magnitude Fg on each other. By what factor you
  multiply the distance between the two objects to
• reduce Fg to 1/16 of its original value?
• Increase Fg nine times of its original value?

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The universal law of gravitation
Gravitational interaction between earth and an
object on or near to its surface
and
m
r
For an object near the surface of the earth r
RE and a g.
ME
RE
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The universal law of gravitation
Mp
Period of Planets
Ms
R
Ms
Law of periods
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The universal law of gravitation

• Example 3
• A weather satellite is in a circular orbit about
  earth. By what factor will the time required for
  a single orbit be multiplied if
• The radius of its orbit is doubled?
• Its mass is tripled?

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Gravitational Potential Energy
m1
r
m2
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Gravitational Potential Energy
Bound system (KE PE) lt 0
Unbound system (KE PE) gt 0
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Gravitational Potential Energy
Escape velocity (speed) (ve) Escape velocity or
speed is the minimum speed that an object must be
propelled from an astronomical body ( planet or
moon) in order to escape its gravitational
attraction.
For a rocket of mass m to escape from a planet or
moon of mass M and radius R, its total energy
must be zero at the surface of the planet or moon.
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The universal law of gravitation
Example 4 Find the escape velocity on earth.
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Exercises

• 8.10,8.12,8.14,8.21,8.32, 8.37, 8.40, 8.71, 8.80