Check out course website for: Link to practice problems & old/sample exams Link to HW website Lecture notes

Transcription

1 Common Exam 1 Time: 4-5:25pm on 9/26, Monday (arrive 15 min before) Room: TBA Covers Week 1 and 2 in the syllabus All problems will be open-ended, no multiple-choice Check out course website for: Link to practice problems & old/sample exams Link to HW website Lecture notes Physics 106 Week 2 Rotational Dynamics I SJ 8 th Ed.: Chap 10.4 to 6 Kinetic energy of rotation Moment of inertia rotational analog of mass Calculating moment of inertia (rotational inertia) Parallel axis theorem definition Examples Torque rotational analog of force Moment arm definition for 2 dimensions Superposition of torques Torque in 3D - Cross product definition Today 2 1

2 Rotational Dynamics We want something like F=ma for rotational motion.. Moment of inertia rotational analog of mass Torque rotational analog of force Goal for today Torque Net torque 3 How to use iclicker 1. Press On/Off button to turn on 2. Frequency setting: Press and hold ON/OFF button until power light flashes. Enter 2 key frequency code : A A 4 2

3 Torque and Moment arm (lever arm) Torque τ measures the effect a force applied at a point has in causing an object to rotate about some axis Torque is a vector, magnitude is: τ = rf sinφ = Fd = rf where F is the force φ is the angle the force makes with the displacement d is the moment arm (or lever arm) of the force d = r sin Φ F = Fsinφ Direction: counterclockwise torque is positive clockwise torque is negative iclicker: Which force will give a greater torque? Axis of rotation is perpendicular to the plane going through the center of bolt head. A) 1 m 90 deg F=2N 2 m 90 deg F=2N B) C) Two torques are equal D) Not enough information 3

4 iclicker: Which force will give a greater torque? Axis of rotation is perpendicular to the plane going through the center of bolt head. F=2N 90 deg 1m A) 180 deg F=10 N B) 1m C) Two torques are equal D) Not enough information iclicker: Which force will give the greatest torque? Axis of rotation is perpendicular to plane, going through the point. All three forces point along the right edge, applied at different points. A B C D. They have the same torque. E. Torque for A and C are equal, greater than B. F. Not enough information. 4

5 Example: Calculate the torque by force F. Axis of rotation is perpendicular to plane, going through the point in the middle of 2 m x 3 m rectangle. F =6 N Example: Calculate the torque by force F. Axis of rotation is perpendicular to plane, going through the point P. Force is applied to a point Q. P 3 m 40 degree Q F =4 N 5

6 Torque vector from r vector and F vector Apply right-hand rule: Curl right hand fingers from r vector direction to F vector direction. Thumb points torque vector direction. y 90 o F φ F φ Frad In this figure, F τ = r F r-direction Cross (vector) product of two vectors Magnitude: Dot (scalar) product A B = ABsinφ AB i = ABcosφ z P r r φ 90 o x line of action of F Direction: by Right Hand Rule Net Torque Add up torque vectors using superposition; i.e. Example: τnet = τ1 +τ τ n F 1 The force will tend to cause a counterclockwise rotation about O The force F will tend to 2 cause a clockwise rotation about O The net torque decides the net effect for rotation. Στ = τ 1 + τ 2 = F 1 d 1 F 2 d 2 same axis 6

7 Example: Seesaw 3m m1 2m m2 30 degree m1=100 kg and m2=70 kg persons are sitting on seesaw. Distance to fulcrum is 2m and 3 m, respectively. The seesaw is tilted at 30 degree from horizontal. A) How many forces are acting on the seesaw plate? B) What is the torque with respect to the fulcrum point from each hf force? C) What is the net torque? 7