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Rotational Motion Part 3

Rotational Motion Part 3. By: Heather Britton. Rotational Motion. Rotational kinetic energy - the energy an object possesses by rotating Like other forms of energy it is expressed in Joules (J). Rotational Motion. Recall that for translational motion KE = (1/2)mv 2 v = ωr

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Rotational Motion Part 3

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  1. Rotational Motion Part 3 • By: Heather Britton

  2. Rotational Motion • Rotational kinetic energy - the energy an object possesses by rotating • Like other forms of energy it is expressed in Joules (J)

  3. Rotational Motion • Recall that for translational motion KE = (1/2)mv2 • v = ωr • Substituting for v we get • KE = (1/2)mω2r2

  4. Rotational Motion • Rearranging we get • KE = (1/2)mr2ω2 • I = mr2 so our equation for rotational KE becomes • KE = (1/2)Iω2

  5. Rotational Motion • In regards to the law of conservation of energy, we now have a new quantity to consider • PEo + KEroto + KEtrano = PE + KErot + KEtran

  6. Example 8 • A tennis ball, starting from rest, rolls down a hill (I = (2/3)mr2). It travels down a valley and back up the other side and becomes airborne at a 35o angle. The height difference between the starting point and launch point is 1.8 m. How far down range will the ball travel in the air?

  7. Rotational Motion • Angular momentum - the rotational analog for linear momentum • Recall p = mv • Substituting for angular quantities we get the equation

  8. Rotational Motion • L = Iω • ω = rotational velocity measured in rad/s • I = moment of inertia measured in kgm2 • L = angular momentum measured in kgm2/s

  9. Rotational Motion • Just like impulse F = p/Δt, there is an analog for rotation • See your book for the derivation of the following equation • τ = Iα

  10. Rotational Motion • The law of conservation of angular momentum - the total angular momentum of a rotating body remains constant if the net torque acting on it is zero

  11. Rotational Motion • Think of a figure skater..... • They spin very fast when they tuck their arms in they spin very fast • When they extend their arms, the rate of rotation slows • Angular momentum is conserved

  12. Example 9 • An artificial satellite is placed into an elliptical orbit about Earth. The point of closest approach (perigee) is rp = 8.37 x 106 m from the center of Earth. The greatest distance (apogee) is ra = 2.51 x 107 m. V at the perigee is 8450 m/s. What is the speed at the apogee?

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