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Rotational Equilibrium and Dynamics

Rotational Equilibrium and Dynamics. Rotational Energy & Rotational Dynamics Problems. Rotational Kinetic Energy. You have learned previously that the mechanical energy of an object includes its translational kinetic energy and its potential energy .

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Rotational Equilibrium and Dynamics

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  1. Rotational Equilibrium and Dynamics Rotational Energy & Rotational Dynamics Problems

  2. Rotational Kinetic Energy • You have learned previously that the mechanical energy of an object includes its translational kinetic energy and its potential energy. • This approach did not consider the possibility that objects could have rotational motion along with translational motion.

  3. Rotational Kinetic Energy • Rotating objects possess kinetic energy associated with their angular speed. • We call this energy rotational kinetic energy. (rotational kinetic energy)=1/2(moment of inertia)x(angular speed)2

  4. Mechanical Energy • Taking rotational motion into account, the mechanical energy of a system is the sum total of the translational kinetic energy, gravitational potential energy, and rotational kinetic energy.

  5. Conservation of Mechanical Energy • Recall that the total energy of a system is conserved.

  6. Analysis of the rolling cans: • Racing identical pop cans. What happens? • What energies do the cans have at the top of the ramp? • At the bottom? • Which has more translational KE? • Which has more rotational KE?

  7. Linear v. Angular Quantities

  8. Sample Problem #1 • A solid ball with a mass of 4.10 kg and a radius of 0.050 m starts from rest at a height of 2.00 m and rolls down a 30.0o slope. What is the translational speed of the ball when it leaves the incline?

  9. Sample Problem #2 • As Halley’s comet orbits the sun, its distance from the sun changes dramatically, from 8.8x1010 m to 5.2x1012 m. If the comet’s speed at closest approach is 5.4x104 m/s, what is its speed when it is farthest from the sun if angular momentum is conserved?

  10. Sample Problem #3 • Assume that a yo-yo has a mass of 6.00x10-2 kg. If a yo-yo descends from a height of 0.600 m down a vertical string and had a linear speed of 1.80 m/s by the time it reached the bottom of the string. If its final angular speed was 82.6 rad/s, what was the yo-yo’s moment of inertia?

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