Conservation of Momentum A system is a pair or group of objects that are interacting in some way. If a system has no external forces acting on it (eg no friction), then the system is isolated. Total momentum in an isolated system is said to be conserved.

? Angular Momentum (L) unit: kgm2s-1 Any rotating object has angular momentum… ?

Angular Momentum Linear momentum DL = t Dt DP = FDt Conservation of L Any rotating object has angular momentum… Angular Momentum Linear momentum DL = t Dt DP = FDt Conservation of L ΣLbefore = ΣLafter (if no net outside torques) Conservation of P ΣPbefore = ΣPafter (if no net outside forces) Compare… Eg “friction torques” Eg “friction forces”

Comparison of linear and rotational motion Quantity Linear Motion Rotational Motion displacement x  velocity v  acceleration a  inertia m I ~ (constant)mr2 kinetic energy Ktrans = 1/2 mv2 Krot = 1/2 I2 momentum p = mv L = I 2nd Law (dynamics) S F = dp/dt S  = dL/dt work W = F|| x W =   conservation law p = 0 if SFext=0 L = 0 if Sext=0 impulse Ft = p  t = L Copyright © 2009, August E. Evrard.

What is the angular momentum of a 20 g, 11 What is the angular momentum of a 20 g, 11.8 cm compact disc spinning at 500 rpm? (use I = ½mr2) m = 0.020 kg r = 0.059 m ω = 500 rev/min = 52.4 rad/s L = Iω = (1/2)mr2ω L = (1/2) 0.020 (0.059)2 · 52.4 L = 0.0018 kgm2rad/s

Which has more angular momentum if both objects have the same rotational velocity? A. B. C. The same D. Can’t be determined

Identical objects are spinning at the same speed, but in opposite directions. Which measurements are the same for both objects? Angular Momentum Rotational Kinetic Energy Both A & B Neither A nor B

 t = L What could you calculate using this L vs t graph to determine the Net Torque? L t Slope of the line Area between the line and the x-axis Y-intercept None of these

A merry-go-round initially spinning clockwise traveling experiences a positive applied torque from the uncle as shown in the graph. Assume Clockwise torques are considered are positive. While traveling the full 0.9 sec, the merry-go-round’s rotational speed: Torque Time (seconds) 0 0.3 0.9 1000 mN 0 mN  t = L first increases and then decreases. first decreases and then increases. continuously increases. drops to zero at 0.9 sec. None of the above. what is the merry-go-round’s change in angular momentum? 0 kg(m2)/sec 10 kg(m2)/sec 300 kg(m2)/sec 450 kg(m2)/sec 900 kg(m2)/sec

 t = L Two identical disks, A and B, initially are spinning on frictionless axles. The initial rotational velocity of Disk A is twice as that of Disk B. You then exert the same constant torque on the two disks over 1 second. One second later, the change in angular momentum of Disk A is: 2ω Non-zero and twice the change in angular momentum of Disk B Non-zero and the same as the change in angular momentum of Disk B Zero. Non-zero and half the change in angular momentum of Disk B Not enough information to determine τ A ω τ B 13