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AP Physics 2013-2014 Unit 8 - Rotation of a Rigid Body Unit Objectives: Understand the uniform circular motion of a particle so you can: Relate the radius of a circle and the speed or rate of revolution of the particle to the magnitude of the centripetal acceleration Describe the direction of the particle’s velocity and acceleration at any instant during the motion Determine the components of the velocity and acceleration vectors at any instant, and sketch or identify graphs of these quantities Use the vector product and the right hand rule to: Calculate the torque of a specified force about an arbitrary origin Calculate the angular momentum vector for a moving particle Calculate the angular momentum vector for a rotating rigid body in simple cases where this vector lies parallel to the angular velocity vector Understand angular momentum conservation so you can: Recognize the conditions under which the law of conservation is applicable and relate this law to one and two particle systems such as satellite orbits State the relationship between net external torque and angular momentum, and identify situations in which angular momentum is conserved Analyze problems in which the moment of inertia of a body is changed as it rotates freely about a fixed axis Analyze a collision between a moving particle and a rigid body that can rotate about a fixed axis or about its center of mass Understand the concept of torque so you can: Calculate the magnitude and sense of the torque associated with a given force Calculate the torque on a rigid body due to gravity Be able to analyze problems in statics so you can: State the conditions for translational and rotational equilibrium of a rigid body Apply these conditions in analyzing the equilibrium of a rigid body under the combined influence of a number of coplanar forces applied at different locations Develop a qualitative understanding of rotational inertia so you can: Determine by inspection which set of symmetrical bodies of equal mass has the greatest rotational inertia Determine by what factor a body’s rotational inertia changes if all its dimensions are increased by the same factor Develop skill in computing rotational inertia so you can find the rotational inertia of: A collection of point masses lying in a plane about an axis perpendicular to the plane A thin rod of uniform density, about an arbitrary axis perpendicular to the rod A thin cylindrical shell about its axis, or a body that may be viewed as being made up of coaxial shells A solid sphere of uniform density about an axis through its center Understand the analogy between translational and rotational kinematics so you can write and apply relations among the angular acceleration, angular velocity, and angular displacement of a body that rotates about a fixed axis with constant angular acceleration Be able to use the right hand rule to associate an angular velocity vector with a rotating body Be able to state and apply the parallel-axis theorem Understand the dynamics of fixed axis rotation so you can: Describe in detail the analogy between fixed axis rotation and straight line translation Describe the angular acceleration with which a rigid body is accelerated about a fixed axis when subjected to a specified external torque or force Apply conservation of energy to problems of fixed axis rotation Analyze problems involving strings and massive pulleys Understand the motion of a rigid body along a surface so you can: Write down, justify, and apply the relation between linear and angular velocity, or between linear and angular acceleration, for a body of circular cross-section that rolls without slipping along a fixed plane, and determine the velocity and acceleration of an arbitrary point on such a body Apply equations of translational and rotational motion simultaneously in analyzing rolling with slipping Unit Outline Date M Jan 13 Day 4 W Jan 15 Day 1 Th Jan 16 Day 2 F Jan 17 Day 3 M Jan 20 No Classes T Jan 21 Day 4 Th Jan 23 Day 1 F Jan 24 Day 2 M Jan 27 Day 3 Topic / Activity Assignments Test Corrections Angular position, velocity, acceleration (Chapter 9) Angular & Translational Quantities Rotational Kinetic Energy ~Science Drop~ ~Martin Luther King Day~ Moment of Inertia Parallel-Axis Theorem Quiz: Angular position, velocity, acceleration Problem Session Torque (Chapter 10) Newton’s 2nd Law Energy in Rotation Work-Energy Theorem T Jan 28 Day 4 Th Jan 30 Day 1 F Jan 31 Day 2 M Feb 3 Day 3 T Feb 4 Day 1 W Feb 5 Early Dismissal Th Feb 6 Day 1 F Feb 7 Day 2 M Feb 10 Day 3 T Feb. 11 Day 4 Th Feb.13 Day 1 F-M Feb 14-17 T Feb. 18 Day 2 Lab Packet: (Series of 3 labs) Lab Packet: (Series of 3 labs) (Cont’d- if needed) AP Problems AP Problems ~Science Drop~ AP Problems MOI Challenge Lab MOI Challenge Lab Problem Session Problem Session Lab: TBD Problem Session ~Faculty Professional Development~ ~President’s Day~ Problem Session HW #24 (due Tue,1/21): pg.299-301 E: #1,3,5,8,9,11,13,15,16,18,21,22, 23,26,29 HW #25 (due Fri, 1/24): pg.301-2 E: #30,31,33,34,35,37,42,43,47,48 HW #26 (due Tue, 1/28): pg. 303 E: #53-57 (all) HW #27: Handout (due Fri, 1/31) HW #28 (due Tue, 2/4): pg. 334-6 P:#1,3,4,8,10,11,12,13,19,20,22,23, 29.31,33,35 HW #29 (due Tue., 2/11): pg. 303-6 P: #64,68,78,83,87,90 Extra Credit :# 95,100 (2 pts each) pg. 338-40 P:#57,61,62,63,70,73,80,81 Complete Analysis Sheets W Feb 19 Day 3 Th Feb.20 Day 4 M Feb. 24 Day 1 ~Science Drop~ TEST: Rotation of a Rigid Body Test Corrections Answers to even #’d problems (from book) are on Haiku…..