Uniform Circular Motion

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Uniform Circular Motion

• Basic Principles Formulas

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Uniform Circular Motion Principles

• Objects move at a constant speed (speed scalar
  quantity)
• Objects velocity is constantly changing (velocity
  vector quantity) due to a continuous change in
  direction
• Velocity is tangent to circular motion
• While in motion, there is a force and an
  acceleration being applied to the object

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Uniform Circular Motion Terms Formulas

• Period (T) time it takes to make 1 revolution
• Period may be given, obvious or determined by
  time/revolutions ex. 25 rev. in 10 sec. T 10/25
  ? .4 sec (T 1/f)
• Frequency (f) number of revolutions made in 1
  sec. (f 1/T) units Hz
• (Period Frequency are Inversely Related)

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Uniform Circular Motion Diagram
Acceleration Force Parallel to Radius /
Velocity Perpendicular to Radius
v
a
r
F
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Uniform Circular Motion Questions

• Q While moving in a circular path, if string
  breaks, in what direction will the object travel?
• A In a straight line, perp. to radius
  (Law of Inertia)
• Q In what direction is the force?
• A Inward
• Q In what direction is the acceleration?
• A Inward

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Uniform Circular Motion Terms Formulas

• Velocity (v) 2pr
• T
• Acceleration (a) 4p²r
• T²
• or v²
• r

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Uniform Circular Motion Terms Formulas

• Force (F) mv²
• r
• or m 4p²r
• T²

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UCM Example Problem

• A 615 kg race car completes 1.00 lap in 14.3 sec
  around a circular track with a radius of 50.0 m.
  What is the cars T, f, v, a, F (on tires)?
• T 14.3/1.00
• 14.3
• f 1.00/14.3
• 0.0699 Hz

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UCM Example Problem (cont.)

• V (2)(p)(50.0)
• 14.3
• 22.0 m/s
• a (22.0 m/s)²
• 50.0
• 9.68 m/s²

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UCM Example Problem (cont.)

• F (on tires) (615 kg)(22.0 m/s)²
• 50.0 m
• 5,950 N