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PHSX213 class. Class stuff MidTerm Exam 2 Wed. March 16 th 8:00 – 9:30 PM Chapters 7-11 Budig 120 (same area as before) Practice Exam Answers on web No classes on Wed., Fri. More on Angular Momentum/Review. Exam Big Picture. Energy Conservation Momentum Conservation
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PHSX213 class • Class stuff • MidTerm Exam 2 • Wed. March 16th 8:00 – 9:30 PM • Chapters 7-11 • Budig 120 (same area as before) • Practice Exam • Answers on web • No classes on Wed., Fri. • More on Angular Momentum/Review
Exam Big Picture • Energy Conservation • Momentum Conservation • Angular Momentum Conservation And understanding the necessary conditions for these to apply.
Exam Stuff : Missing Equations • Krot = ½ I w2 • w = v/r ; atan = a r • Emech = K + U • DEmech = WNC • Exam will be 25 multiple choice questions. • Time = 90 minutes (not 150 mins)
Clarification • On Friday, we were discussing how to calculate the net torque. • One has to calculate this consistently with respect to the same point. In general, it is really only useful to calculate it about the rotation axis. • Only for the special case of equilibrium, where the net force is zero, does one have the freedom to choose the reference point.
Check-Point 1 • The motion of two balls before and after a collision is shown. Ball 1 chases Ball 2. The speed of Ball 1 is 4 m/s and the speed of Ball 2 is 3 m/s. After the collision Ball 1 rebounds at 3 m/s, and Ball 2 speeds away at 4 m/s. The mass of each ball is 1 kg. Which one statement is true ? • A) Momentum was not conserved during the collision, so there must have been some external force acting that we’re not told about. • B) Kinetic energy was not conserved during the collision • C) The momentum change for Ball 1 is +7 kg m/s • D) The momentum change for Ball 2 is +7 kg m/s • E) All of the above are true. after before +x 2 1 2 1
Torque Definition for a Particle t = r F Vector product means that the torque is directed perpendicular to the plane formed by (r, F). Whether it is up or down is from the right-hand rule convention NB Only makes sense to talk about the torque wrt or about a certain point
Angular Momentum Definition for a Particle l = r p = r m v NB Only makes sense to talk about the angular momentum wrt or about a certain point
Angular Momentum Definition for a Rigid Body About a Fixed Axis L = Sli = I w In analogy to P = M v
Newton II for Rotation • S F = dp/dt ( the general form of Newton II) • St = dl/dt • It is the net torque that causes changes in angular momentum.
Angular Momentum Conservation • Just as for Newton II for linear motion where if the net force was zero, dp/dt =0 => p conserved. • For rotational motion, if the net torque is zero, dl/dt =0, so l conserved.
Angular Momentum Conservation Problems This is a situation where using both the particle and rigid body definitions of angular momentum is useful.
Kepler’s Second Law Each planet moves so that a line drawn from the Sun to the planet sweeps out equal areas, A, in equal periods of time. ie. dA/dt = 0
Check-Point 2 • The angular momentum vector of Earth about its rotation axis, due to its daily rotation, is directed: • A. tangent to the equator toward the east • B. tangent to the equator toward the west • C. north • D. southwest • E. towards the Sun