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) 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)mv 2 v = ωr Substituting for v we get KE = (1/2)mω 2 r 2 Recall that for translational motion KE = (1/2)mv 2 v = ωr Substituting for v we get KE = (1/2)mω 2 r 2

4. Rotational Motion Rearranging we get KE = (1/2)mr 2 ω 2 I = mr 2 so our equation for rotational KE becomes KE = (1/2)Iω 2 Rearranging we get KE = (1/2)mr 2 ω 2 I = mr 2 so our equation for rotational KE becomes KE = (1/2)Iω 2

5. Rotational Motion In regards to the law of conservation of energy, we now have a new quantity to consider PE o + KE roto + KE trano = PE + KE rot + KE tran In regards to the law of conservation of energy, we now have a new quantity to consider PE o + KE roto + KE trano = PE + KE rot + KE tran

6. Example 8 A tennis ball, starting from rest, rolls down a hill (I = (2/3)mr 2 ). It travels down a valley and back up the other side and becomes airborne at a 35 o 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 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 kgm 2 L = angular momentum measured in kgm 2 /s L = Iω ω = rotational velocity measured in rad/s I = moment of inertia measured in kgm 2 L = angular momentum measured in kgm 2 /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 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 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 r p = 8.37 x 10 6 m from the center of Earth. The greatest distance (apogee) is r a = 2.51 x 10 7 m. V at the perigee is 8450 m/s. What is the speed at the apogee?