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John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw

Physics 114A - Mechanics Lecture 23 (Walker: Ch. 10.1-3) Rotational Kinematics February 24, 2014. John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu. Announcements.

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John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw

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  1. Physics 114A - MechanicsLecture 23 (Walker: Ch. 10.1-3)Rotational KinematicsFebruary 24, 2014 John G. Cramer Professor Emeritus, Department of Physics B451 PAB jcramer@uw.edu

  2. Announcements • HW#7 is due at 11:59 PM on Thursday, February 27. HW#8 is due at 11:59 PM on Thursday, March 6, the day before Exam 3. • Check your Exam 2 section scores on WebAssign under to make sure you have credit for both sections. The Exam 2 Solutions are available from the Physics 114A Course Schedule by clicking on “Exam 2”. Regrade requests must be turned in to Susan Miller (C136 PAB) through 4 PM today. • My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A (this building). Physics 114A - Lecture 23

  3. Lecture Schedule (Part 3) We are here. Physics 114A - Lecture 23

  4. Circular Motion Physics 114A - Lecture 23

  5. A Particle inUniform Circular Motion For a particle in uniform circular motion, the velocity vector v remains constant in magnitude, but it continuously changes its direction. However, at each position it is tangent to the circular path. For this reason, it is called the tangential velocity of the particle. Physics 114A - Lecture 23

  6. Angular Position q Physics 114A - Lecture 23

  7. Angular Position q Degrees and revolutions: Physics 114A - Lecture 23

  8. Angular Position q Arc length s, measured in radians: Physics 114A - Lecture 23

  9. Angular Velocity w Physics 114A - Lecture 23

  10. Graphical Representationof Circular Motion This figure shows the angular position of a particle moving around a circle of radius r. Graph the angular velocity w of the particle. Physics 114A - Lecture 23

  11. Rotational Period T Example: Find the period of a music phonograph record that is rotating at 45 RPM. Physics 114A - Lecture 23

  12. Angular Acceleration a Physics 114A - Lecture 23

  13. Example: Decelerating Windmill As the wind dies, a windmill that had been rotating at w = 2.1 rad/s begins to slow down at a constant angular acceleration of a = -0.45 rad/s2. How long does it take for the windmill to come to a complete stop? Physics 114A - Lecture 23

  14. Angular Speed & Acceleration Accelerating Decelerating Physics 114A - Lecture 23

  15. Clicker Question 1 The fan blade shown is slowing down. Which option describes a and w? (c) w<0 and a>0; (d) w<0 and a<0. (a) w>0 and a>0; (b) w>0 and a<0; Physics 114A - Lecture 23

  16. Summary of Angular Variables Physics 114A - Lecture 23

  17. Plotting a and w The angular acceleration a is the rate of change of the angular velocity w. If the angular acceleration a and the angular velocity w are plotted vs. time t, then ais the slope of the w vs. t curve, and Dw=w(tf) - w(ti)is the area under the a vs. t curve in the time interval between ti and tf. Physics 114A - Lecture 23

  18. Rotational Kinematics If the angular acceleration is constant: Physics 114A - Lecture 23

  19. Rotational vs. Linear Kinematics Analogies between linear and rotational kinematics: Physics 114A - Lecture 23

  20. Example: Thrown for a Curve To throw a curve ball, a pitchergives the ball an initial angularspeed of 36.0 rad/s. When thecatcher gloves the ball 0.595 slater, its angular speed hasdecreased (due to air resistance)to 34.2 rad/s. (a) What is the ball’s angular acceleration, assuming it to be constant? (b) How many revolutions does the ball make before being caught? Physics 114A - Lecture 23

  21. Example: Wheel of Misfortune On a certain game show, contestants spin thewheel when it is their turn. One contestant givesthe wheel an initial angular speed of 3.40 rad/s.It then rotates through 1.25 revolutions andcomes to rest on BANKRUPT. (a) Find the wheel’s angular acceleration,assuming it to be constant. (b) How long does it take for the wheel tocome to rest? Physics 114A - Lecture 23

  22. Example: A Rotating Crankshaft A car’s tachometer indicates the angular velocityw of the engine’s crankshaft in rpm. A car stopped ata traffic light has its engine idling at 500 rpm. When thelight turns green, the crankshaft’s angular velocity speeds upat a constant rate to 2,500 rpm in a time interval of 3.0 s. How many revolutions does the crankshaft make in this time interval? Physics 114A - Lecture 23

  23. Example: Time to Rest A pulley rotating in the counterclockwise direction is attached to a mass suspended from a string. The mass causes the pulley’s angular velocity to decrease with a constant angular acceleration a = -2.10 rad/s2. (a) If the pulley’s initial angular velocity is w0 = 5.40 rad/s, how long does it take for the pulley to come to rest? (b) Through what angle does the pulley turn during this time? Physics 114A - Lecture 23

  24. Connections BetweenLinear & Rotational Quantities The tangential velocity vt is zero at the center of rotation and increases linearly with r. Physics 114A - Lecture 23

  25. Example: CD Speed Unlike old phonograph records that turned with a constant angular speed (like 33⅓ rpm), CDs and DVDs turn with a variable w that keeps the tangential speed vt constant. Find the angular speed w that a CD must have in order to give it a linear speed vt= 1.25 m/s when the laser beam shines on the disk(a) at 2.50 cm from its center, and(b) at 6.00 cm from its center. Physics 114A - Lecture 23

  26. Connections BetweenLinear & Rotational Quantities Question:Two children ride a merry-go-round, with Child 1 at a greater distance from the axis of rotation than is Child 2. How do the angular speeds w1,2 of the two children compare? (a) w1>w2 (b) w1=w2 (c) w1<w2 Physics 114A - Lecture 23

  27. Connections BetweenLinear & Rotational Quantities Question:Two children ride a merry-go-round, with Child 1 at a greater distance from the axis of rotation than is Child 2. How do the angular speeds w1,2 of the two children compare? (a) w1>w2 (b) w1=w2 (c) w1<w2 Physics 114A - Lecture 23

  28. Connections BetweenLinear & Rotational Quantities Physics 114A - Lecture 23

  29. Speeding up Connections BetweenLinear & Rotational Quantities This merry-go-round has both tangential and centripetal acceleration. Physics 114A - Lecture 23

  30. End of Lecture 23 • Regrade requests for Exam 2 must be turned in to Susan Miller (C136 PAB) through 4 PM today. • Homework Assignment #7 is due at 11:59 PM on Thursday, February 27. • My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the “114” area of the Physics Study Center on the Mezzanine floor of PAB A. Physics 114A - Lecture 23

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