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Circular motion

Circular motion. Measuring Circular Motion (Method 1). 1 complete rotation = 1 revolution Measure rotational motion by counting the number of rotations Most common unit of measurement = revolution (abbreviated rev ). Measuring Circular Motion (Method 2). 360°.

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Circular motion

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  1. Circular motion

  2. Measuring Circular Motion (Method 1) • 1 complete rotation = 1 revolution • Measure rotational motion by counting the number of rotations • Most common unit of measurement = revolution (abbreviated rev)

  3. Measuring Circular Motion (Method 2) 360° • Can also measure using degrees • 1 rotation = 1 revolution = 360°

  4. Measuring Circular Motion (Method 3) Θ=s/r • Radian (rad): angle with vertex at center of circle whose sides cut off an arc on circle equal to its radius • Radius = r • Length of arc = s • angle = 1 radian • Unitless dimension – use rad to avoid confusion

  5. Converting between different measurement • By definition: 1 rev = 360° = 2πrad • Convert 10πrad to revolutions

  6. Converting from Degree to Rad • θrad=(π/180)θdegrees • Convert 75 degrees to radians

  7. Angular Displacement • Distance through which any point on rotating body moves (angular distance instead of linear distance) • Example: when a wheel makes one complete rotation, it’s angular displacement has been 1 rev, 2πrad, or 360°

  8. Angular Velocity • Similar to linear velocity, except instead of linear displacement, use angular displacement • Angular velocity = rev/time • OR ω = angular displacement (θ)/time (t) • Units = rad/s or rev/min θ t ω =

  9. Example • A motorcycle wheel turns 7200 times while being ridden for 10 min. What is the angular velocity in rev/min?

  10. Linear Velocity • The linear speed on any point on rotating circle = v = ωr v = linear velocity ω = angular velocity r = radius • Can measure using stroboscope or strobe light

  11. Example: Linear Velocity A wheel of 1.00 m radius turns at 1000 rpm. Find the linear speed of a point on the rim of the wheel.

  12. Angular Acceleration Angular acceleration = rate of change of angular velocity α = angular acceleration Δω = change in angular velocity t = time Δω t α =

  13. Equations: Linear vs. Rotational Motion

  14. Sample Calculations • To calculate various components of angular motion, click on the link listed below: http://canario.iqm.unicamp.br/MATDID/HyperPhysics/hbase/rotq.html

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