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Test 2 Thursday, March 25 8:20 pm Covers: Ch. 6, Ch. 7, Secs. 8.1-8.5 Bring: calculator, ID, formula sheet (no phones! formula sheet: 2-sided, handwritten) Last name A-G H-M N-U V-Z Room TUR L007 CLB C130 WEIM 1064 LIT 0113 Office hours canceled this week: Hirschfeld, Chan (and next Mon), Acosta, Goswami, Sabri, Dashti, Timmerwilke, Dasbiswas Discussion Sections meet as usual Ch. 8 General Torque Formula Component of F r OR r F sin • The lever arm, d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force d = r sin so = F d = F r sin Torque and Equilibrium • First Condition of Equilibrium • The net external force must be zero F 0 or Fx 0 and Fy 0 •The Second Condition of Equilibrium states The net external torque must be zero 0 In-class quiz A meter stick has a fulcrum at its midpoint. A 100 gram weight is hanging 20 cm from the fulcrum. A second weight is balancing at a spot 50 cm from the other side of the fulcrum. What is the mass of the second weight? A. 40 gm B. 30 gm C. 20 gm D. 5 gm E. 2 gm Center of mass and of gravity • If an object is “symmetrical’’ then the center of mass is just where you think that it should be. • If an object is “complicated” then r m MRCoM The torque from gravity is “as if” the force of gravity acts only at the CoM Balancing Objects • If an object is hanging freely from an axis, then the CoM must be directly beneath the axis. • If a solid object is standing up, then the CoM must be over the base of the object. • A larger base is more stable. Example of a Free Body Diagram--Ladder L free body diagram shows normal force and force of static friction acting on the ladder at the ground The last diagram shows the lever arms for the forces from axis of rotation at ground Pick axis and sum torques Torque and Angular Acceleration Newton’s Second Law for a Rotating Object I analogous to ∑F = ma I = moment of inertia 2 2 I m r MR For Uniform Ring i i moment of inertia depends on quantity of matter and its distribution and location of axis of rotation Other Moments of Inertia Newton’s Second Law for Rotation-- Example • Draw free body diagrams of each object • Only the cylinder is rotating, so apply = I • The bucket is falling, but not rotating, so apply F = ma • Remember a = r and solve the resulting equations In-class quiz What is the torque applied to the reel by the cord? A. B. C. D. mgR 0 TR MgR Torque and Angular Acceleration I ∑F = ma T - mg = ma 12 Ma mg ma mg a M m 2 2 1 RT 2 MR R a R/ T 12 MR/ a Look at a as m0 or or M0 or