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ENERGY and ROTATION

ENERGY and ROTATION. Rotational kinematics, part 3. Kinetic Energy of Rotation. Rotational KE is similar to translational KE depends on how fast you move depends on the size of the object Cannot say K=½mv 2 since each particle in a body can have a different speed Therefore,

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ENERGY and ROTATION

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  1. ENERGY and ROTATION Rotational kinematics, part 3

  2. Kinetic Energy of Rotation • Rotational KE is similar to translational KE • depends on how fast you move • depends on the size of the object • Cannot say K=½mv2 since each particle in a body can have a different speed • Therefore, • Since the expression for Krotational becomes • Finally, given our definition of moment of inertia

  3. Example • A cylinder on mass M and radius R rolls (w/o slipping) down an incline plane as shown. • Assuming the cylinder starts from rest at the top of the incline, what is the linear speed of its CM at the bottom? STRATEGY: Apply energy conservation

  4. Example (cont’d) • Since • and • the energy conservation expression becomes Solving for vCM yields

  5. Another example • A 5kg block is hung from a pulley with a radius of 15cm and a mass of 8kg. The block is then released from rest. • What is the speed of the block when it hits the floor 2m below? • What is Krotational just before the block hits the floor?

  6. STRATEGY: Apply energy conservation

  7. The rotational kinetic energy of the pulley is simply

  8. Work & Power • Recall that W=FDs • In rotational kinematics, Ds=rDq • By substitution, W=FrDq=tDq • If we consider variable torques, then the work done is an integral • The work-energy theorem is true even if the work is done by a net torque: W=DKrotational

  9. Power • It’s still the rate at which work is done • Over a small angular displacement dq, the torque t does a small amount of work dW. • Therefore, • Again we see the parallels between rotational and linear kinematics --- this expression is analogous to P=Fv

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