Chap' 7 Dynamics III: Motion in a Circle

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Chap. 7 Dynamics IIIMotion in a Circle

• 7.1 Uniform Circular Motion
• 7.2 Velocity and Acceleration in Uniform Circular
  Motion
• 7.3 Dynamics of Uniform Circular Motion
• 7.4 Circular Orbital
• 7.6 Nonuniform Circular Motion

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Uniform Circular Motion

• Period
• Angular Position

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Angular Velocity

• Average angular velocity ??/?t
• Instantaneous angular velocity
• The angular velocity is constant during uniform
  circular motion

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An old-fashioned single-play vinyl record rotates
30.0 rpm . What are (a) the angular velocity in
rad/s and (b) the period of the motion?

• rpm revolution per minute.
• 1 rpm 2p/60 (rad)/s

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Velocity and acceleration in uniform circular
motion
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Velocity in uniform circular motion
The magnitude of velocity is a constant V r
d?/dt?r
Has only a tangential Component
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Centripetal acceleration
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The magnitude of centripetal acceleration
P184
Towards center of circle
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Dynamics of Uniform Circular Motiion

• From the Newtons second law, a particle of mass
  m moving at constant speed V around a circle of
  radius r must have a net force of
• magnitude (mV2/r) pointing toward the center
  of the circle

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The Conical Pendulum

• A small object of mass m is suspended from a
  string of length L.
• how many forces act on the object when it
  revolved with constant speed V in a horizontal
  circle?

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Turning the corner
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Circular Orbits
The real weight force is always directed Toward
the center of the planet
downwards
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Nonuniform circular motion
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Tangential acceleration
Change the speed
Here a is angular acceleration
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Dynamics of nonuniform circular motion
The radial force causes the Centripetal
acceleration. It makes Velocity change direction.
The tangential force causes The tangential
acceleration. It Makes speed change
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Ex. P.47 Passenger stand inside a 16-m-diamete
rotation ring.After the ring has acquired
sufficient speed, It tilts into a vertical plane,
as shown in the Figure
At the top
At the bottom