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Chapter 8

Chapter 8. Rotational Motion. q. Rotational Motion. Angular Distance ( q ) Replaces distance for rotational motion Measured in Degrees Radians Revolutions. Radian Measure. r. r. 1 rad. r. 1 rad = 57.3 degrees 2 p rad in one circle. Windows Calculator. w. Rotational Motion.

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Chapter 8

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  1. Chapter 8 Rotational Motion

  2. q Rotational Motion • Angular Distance (q) • Replaces distance for rotational motion • Measured in • Degrees • Radians • Revolutions

  3. Radian Measure r r 1 rad r 1 rad = 57.3 degrees 2p rad in one circle

  4. Windows Calculator

  5. w Rotational Motion • Speed of Rotation (w) • w = Angle covered/Time required • = Dq/Dt • Note similarity to v = Dx/Dt • Measured in • degrees/second • radians/second • revolutions/second

  6. Rotational Motion • Angular Acceleration - Measures how angular velocity is changing (a) • a = Dw/Dt Note similarity to a = Dv/Dt • Measured in … • degrees/s2 • radians/s2 • revolutions/s2

  7. Rotational Inertia • Property of an object that resists changes in rotation • For linear motion mass was a measure of inertia • For rotational motion Moment of Inertia (I) is the measure of rotational Inertia

  8. Moments of Inertia • Depends on … • Mass of the Object • Axis of Rotation • Distribution of Mass in the Object

  9. Moments of Inertia Standard Shapes

  10. Moment of Inertia • Inertia Bars • Ring and Disk on Incline • Metronome • People walking • Weighted Stick - Bare Stick

  11. Torque • Product of Force and Lever Arm • Torque = Force X Lever Arm • Examples: • Balance • See-Saw • Wrench

  12. W1d1 = W2d2

  13. Sample Torque Problem (0.5 kg)(9.8 m/s2)(0.1 m) = (0.2 kg)(9.8 m/s2)d

  14. Lever Arm F Line of Action

  15. Torque Examples

  16. Torque • Just as unbalanced forces produce acceleration, unbalanced torques produce angular acceleration. • Compare: SF = ma St = Ia

  17. Center of Mass • Average position of the mass of an object • Newton showed that all of the mass of the object acts as if it is located here. • Find cm of Texas/USA

  18. Finding the Center of Mass Line of action Pivot point Lever arm No Torque Torque weight

  19. High Jumper

  20. Stability • In order to balance forces and torques, the center of mass must always be along the vertical line through the base of support. • Demo • Coke bottle • Chair pick-up

  21. Base of Support Stability

  22. Stability • Which object is most stable?

  23. Centripetal Force • Any force that causes an object to move in a circle. • Examples: • Carousel • Water in a bucket • Moon and Earth • Coin and hanger • Spin cycle

  24. Centripetal force F = mac = mv2/r = mrw2

  25. Centrifugal force • Fictitious center fleeing force • Felt by object in an accelerated reference frame • Examples: • Car on a circular path • Can on a string

  26. Space Habitat(simulated gravity) w r

  27. Space Habitat(simulated gravity) • “Down” is away from the center • The amount of “gravity” depends on how far from the center you are.

  28. Angular Momentum L = (rotational inertia) X (angular velocity) L = Iw Compare to linear momentum: p = mv

  29. Linear Momentum and ForceAngular Momentum and Torque • Linear SF = Dp/Dt • Impulse Dp = SF Dt • Rotational St = DL/ Dt • Rotational Impulse DL = St Dt

  30. Conservation of Momentum • Linear • If SF = 0, then p is constant. • Angular • If St = 0, then L is constant.

  31. Conservation of Angular Momentum • Ice Skater • Throwing a football • Rifling • Helicopters • Precession

  32. Rifling

  33. Football Physics L

  34. Helicopter Physics Rotation of Rotor Body Rotation Tail rotor used to produce thrust in opposite direction of body rotation

  35. Precession

  36. Age of Aquarius

  37. Linear - Rotational Connections Linear Rotational x (m) q (rad) v (m/s) w (rad/s) a (m/s2) a (rad/s2) m (kg) I (kg·m2) F (N) t (N·m) p (N·s) L (N·m·s)

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