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Physics 218 Lecture 19. Dr. David Toback. Rotational Motion. Last lecture on Chapters 9 & 10 We’ll work on hard problems to try and cover the main topics Will use these topics for Chap 11: Statics Exam 3 Coming up soon: November 21 st Tuesday before Thanksgiving Covers Chapters 8-11.

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## Physics 218 Lecture 19

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**Physics 218Lecture 19**Dr. David Toback Physics 218, Lecture XIX**Rotational Motion**• Last lecture on Chapters 9 & 10 • We’ll work on hard problems to try and cover the main topics • Will use these topics for Chap 11: Statics • Exam 3 • Coming up soon: November 21st • Tuesday before Thanksgiving • Covers Chapters 8-11 Physics 218, Lecture XIX**A bullet strikes a cylinder**A bullet of speed V and mass m strikes a solid cylinder of mass M and moment of 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? Physics 218, Lecture XIX**Rolling Down an Incline**A solid ball of mass m and radius R starts from rest and rolls without slipping down a plane with height Z. Using forces, what will be the final speed of the ball? Note: Isphere = 2/5MR2 Z Physics 218, Lecture XIX**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 XIX**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 XIX**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. We note that there is friction in the system. This gives a torque (due to the axel) we’ll call this tfric. What is the moment of Inertia? R Physics 218, Lecture XIX**Next Week**• Chapter 11 (Statics) and 12 (Gravity) • No reading questions… If I think people haven’t done the reading I’ll just give an in-class quiz • Statics will be on exam 3 (last topic) • Please get caught up on the homework!!! • HW10 due on Monday • Exam 3 is November 21st • Tuesday before Thanksgiving! Physics 218, Lecture XIX**End of Lecture Notes**Physics 218, Lecture XIX**A bullet strikes a cylinder**A bullet of speed V and mass m strikes a solid cylinder of mass M and moment of 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 XIX**Kepler’s 2nd Law**2nd Law: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out area in equal periods of time Physics 218, Lecture XIX**Atwood’s Machine**A pulley with a fixed center (at point O), radius R0 and moment of inertia I, has a massless rope wrapped around it (no slipping). The rope has two masses, m1 and m2 attached to its ends. Assume m2>m1 • What is the acceleration of the system? • Do some checks. Physics 218, Lecture XIX**Same Problem: Forces**Same problem but with Forces Physics 218, Lecture XIX**Next Period: Exam 3 Review**• Exam: • Problems similar to those from the Textbook, Homework and Lecture • Formula sheet handed out • All formulas you use must be derived from those on the formula sheet • Topics are: Chapters 8-10 • Conservation of Energy • Momentum and Collisions • Rotational Motion • Today’s Topics not covered, but are a review Physics 218, Lecture XIX**Extra Credit**For exam 3, there are now a possible 5 extra credit points available to you if you complete the following before the exam: • Have a 100 on all HW and HWq up to, and including, CH10 as well as the math quizzes. • When you do, a mini-practice exam will become available to you. • You can take as many mini-practice exams as you like until you get a 100 • If you get a 100, you will get 5 extra credit points Physics 218, Lecture XIX**Why does the Bicycle Wheel Turn to the Right?**Physics 218, Lecture XIX**Angular Momentum**Again we use the Cross Product: Derivation of St = dL/dt Physics 218, Lecture XIX**L for a system of many bodies**• Have to be careful with Angular Momentum • t = dl/dt for a single particle • St = S(dl/dt) for a system of many particles • All internal torques cancel because of Newton’s law (all internal forces are equal and opposite) • Reference Frame matters. Only true for: • The origin is an inertial Reference Frame • The center of mass Physics 218, Lecture XIX**L for a Rigid Body**Find the angular momentum, L, for this body given that it is rotating around the Z axis with angular velocity w. Physics 218, Lecture XIX

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