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ENGR 215 ~ Dynamics Sections 15.5 – 15.7

ENGR 215 ~ Dynamics Sections 15.5 – 15.7. Angular Momentum. “Moment” of the particle’s linear momentum about Point O. Scalar Formulation If the particle is moving along a curve lying in the x-y plane. Angular Momentum. Vector Formulation If the particle is moving along a space curve.

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ENGR 215 ~ Dynamics Sections 15.5 – 15.7

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  1. ENGR 215 ~ Dynamics Sections 15.5 – 15.7

  2. Angular Momentum • “Moment” of the particle’s linear momentum about Point O. • Scalar Formulation • If the particle is moving along a curve lying in the x-y plane.

  3. Angular Momentum • Vector Formulation • If the particle is moving along a space curve.

  4. Lecture Example 1: Determine the angular momentum HO of the particle about Point O.

  5. Relation between Moment of a Force and Angular Momentum

  6. Relation between Moment of a Force and Angular Momentum • The time rate of change of a particle’s angular momentum is equal to the torque acting on it. • The time rate of change of a particle’s linear momentum is equal to the force acting on it.

  7. Angular Impulse & Momentum Principles

  8. Linear and Angular Impulse

  9. Conservation of Angular Momentum • When the angular impulses acting on a particle are all zero during a time from t1 to t2, angular momentum is conserved.

  10. Lecture Example 2: A 4-lb ball is traveling around a circle of radius r = 3 ft with a speed (vb)1 = 6 ft/s. If the cord is pulled through the hole with a constant speed, determine the speed of the ball when r = 2 ft. Also, how much work had to be done to pull down the cord?

  11. Lecture Example 3: The 800-lb roller-coaster starts from rest on the track having the shape of a cylindrical helix. It the helix descends 8 ft for every revolution, determine the time required for the car to attain a speed of 60 ft/s. Neglect friction and the size of the car,

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