Physics 218 Lecture 18 Dr. David Toback Physics 218, Lecture XVIII

Announcements Chapter 9 HW due Wed Nov 8th Chapter 10 HW due Monday Nov 13th, as usual First Announcement of Exam 3: November 21st Tuesday before Thanksgiving! Physics 218, Lecture XVIII

Rotational Motion Chapters 9 and 10 in four lectures Lecture three of the four lectures Concentrate on the relationship between linear and angular variables Today: Finish up topics Thursday: Hard problems Physics 218, Lecture XVIII

Physics 218, Lecture XVIII

Angular Quantities Position  Angle q Velocity  Angular Velocity w Acceleration  Angular Acceleration a Force  Torque t Mass  Moment of Inertia I Today we’ll finish: Momentum Energy Physics 218, Lecture XVIII

Momentum Momentum vs. Angular Momentum: Newton’s Laws: Physics 218, Lecture XVIII

Angular Momentum First way to define the Angular Momentum L: Physics 218, Lecture XVIII

Angular Momentum Definition Another definition: Physics 218, Lecture XVIII

Angular Motion of a Particle Determine the angular momentum, L, of a particle, with mass m and speed v, moving in circular motion with radius r Physics 218, Lecture XVIII

Conservation of Angular Momentum By Newton’s laws, the angular momentum of a body can change, but the angular momentum for a system cannot change Conservation of Angular Momentum Same as for linear momentum Physics 218, Lecture XVIII

Ice Skater This one you’ve seen on TV Try this at home in a chair that rotates Get yourself spinning with your arms and legs stretched out, then pull them in Physics 218, Lecture XVIII

BEFORE and AFTER Problem Solving For Conservation of Angular Momentum problems: BEFORE and AFTER Physics 218, Lecture XVIII

Conservation of Angular Momentum Before Physics 218, Lecture XVIII

Conservation of Angular Momentum After Physics 218, Lecture XVIII

Clutch Design As a car engineer, you model a car clutch as two plates, each with radius R, and masses MA and MB (IPlate = ½MR2). Plate A spins with speed w1 and plate B is at rest. you close them so they spin together Find the final angular velocity of the system Physics 218, Lecture XVIII

Angular Quantities Position  Angle q Velocity  Angular Velocity w Acceleration  Angular Acceleration a Force  Torque t Mass  Moment of Inertia I Today we’ll finish: Momentum  Angular Momentum L Energy Physics 218, Lecture XVIII

Rotational Kinetic Energy KEtrans = ½mv2  KErotate = ½Iw2 Conservation of Energy must take rotational kinetic energy into account Physics 218, Lecture XVIII

Rotation and Translation Objects can both Rotate and Translate Need to add the two KEtotal = ½ mv2 + ½Iw2 Rolling without slipping is a special case where you can relate the two V = wr Physics 218, Lecture XVIII

Rolling Down an Incline You take a solid ball of mass m and radius R and hold it at rest on a plane with height Z. You then let go and the ball rolls without slipping. What will be the speed of the ball at the bottom? What would be the speed if the ball didn’t roll and there were no friction? Note: Isphere = 2/5MR2 Z Physics 218, Lecture XVIII

A bullet strikes a cylinder A bullet of speed V and mass m strikes a solid cylinder of mass M and inertia I=½MR2, at radius R and sticks. The cylinder is anchored at point 0 and is initially at rest. What is w of the system after the collision? Is energy Conserved? Physics 218, Lecture XVIII

Rotating Rod A rod of mass uniform density, mass m and length l pivots at a hinge. It has moment of inertia I=ml/3 and starts at rest at a right angle. You let it go: What is w when it reaches the bottom? What is the velocity of the tip at the bottom? Physics 218, Lecture XVIII

Less Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force FT. It accelerates to final angular speed w in time t. A better estimate takes into account that there is friction in the system. This gives a torque (due to the axel) we’ll call this tfric. What is this better estimate of the moment of Inertia? R Physics 218, Lecture XVIII

Person on a Disk A person with mass m stands on the edge of a disk with radius R and moment ½MR2. Neither is moving. The person then starts moving on the disk with speed V. Find the angular velocity of the disk Physics 218, Lecture XVIII

Same Problem: Forces Same problem but with Forces Physics 218, Lecture XVIII

Next Time Please get caught up on homework!!! More problems on Chapters 9 & 10 Please get caught up on homework!!! Believe it or not exam 3 is just around the bend, Nov 21st Tuesday before Thanksgiving! Chap 9 HW due Wednesday Nov 8th Chap 10 HW due Nov 13th Physics 218, Lecture XVIII

End of Lecture Notes Physics 218, Lecture XVIII

Exam II Mean = 75 Average on first two exam = 76% Please check to make sure they added your points correctly AND entered them into WebCT correctly!!! Average on first two exam = 76% Straight scale so far… Reading quizzes should be passed back in recitation Physics 218, Lecture XVIII

Next Time Reading Questions: Q11.X & Q11.X XXX FIXME!!! Chapter 11 Reading Questions: Q11.X & Q11.X XXX FIXME!!! Math, Torque, Angular Momentum, Energy again, but more sophisticated The material will not be on the 3rd exam, but will help with the exam. It will all be on the final HW 10 Due Monday Exam 3 is next Thursday, April 22nd Physics 218, Lecture XVIII

Angular Quantities Position  Angle q Velocity  Angular Velocity w Acceleration  Angular Acceleration a Force  Torque t Today we’ll finish: Mass Momentum Energy Physics 218, Lecture XVIII

Calculating Moments of Inertia Here r is the distance from the axis of each little piece of mass Physics 218, Lecture XVIII

Calculate the Moment of Inertia A pulley has mass M, uniform density, radius R, and rotates around its fixed axis Calculate its moment of inertia R Physics 218, Lecture XVIII

Calculate the Moment of Inertia Better example here… Calculate its moment of inertia R Physics 218, Lecture XVIII

Physics 218, Lecture XVIII

Hollow Cylinder Consider a hollow cylinder with uniform density, inner radius R1, outer radius R2 and total Mass M. Find the moment of Inertia Physics 218, Lecture XVIII

Parallel-Axis Theorem Quick Trick for calculating Moments I = Icm + Mh2 Example Physics 218, Lecture XVIII