1 / 23

Rotational Kinematics

Rotational Kinematics. Circular Motion. A Particle in Uniform Circular Motion. For a particle in uniform circular motion, the velocity vector v remains constant in magnitude, but it continuously changes its direction. Angular Position: θ. Angular Position q. Degrees and revolutions:.

Samuel
Télécharger la présentation

Rotational Kinematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rotational Kinematics

  2. Circular Motion

  3. 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.

  4. Angular Position: θ

  5. Angular Position q Degrees and revolutions:

  6. Angular Position q Arc length s, measured in radians:

  7. Angular Velocity w

  8. Sign of 

  9. Connections BetweenLinear & Rotational Quantities

  10. Angular Acceleration a

  11. Comparison to 1-D Kinematics Angular Linear And for a point at a distance R from the rotation axis: • x = Rv = R a = R By convention, , ,  are positive if they are in the counterclockwise direction.

  12. 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?

  13. Angular Velocity & Acceleration ACT 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;

  14. Rotational Kinematics If the angular acceleration is constant:

  15. Thrown for a Curve To throw a curve ball, a pitchergives the ball an initial angularspeed of 157.0 rad/s. When thecatcher gloves the ball 0.795 slater, its angular speed hasdecreased (due to air resistance)to 154.7 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?

  16. 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?

  17. A Rotating Crankshaft A car’s tachometer indicates the angular velocity w of the crank shaft in rpm. A car stopped at a traffic light has its engine idling at 500 rpm. When the light turns green, the crankshaft’s angular velocity speeds up at a constant rate to 2500 rpm in a time interval of 3.0 s. How many revolutions does the crankshaft make in this time interval?

  18. 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? • Through what angle does the pulley turn during this time? (c) If the radius of the pulley is 5.0 cm, through what distance is the mass lifted?

  19. CD Speed CDs and DVDs turn with a variable w that keeps the tangential speed vt constant. Find the angular speed w and the frequency 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.

  20. Rotational vs. Linear Kinematics Analogies between linear and rotational kinematics:

  21. Connections BetweenLinear & Rotational Quantities

  22. Speeding up More Connections BetweenLinear & Rotational Quantities This merry-go-round has both tangential and centripetal acceleration.

  23. The Microhematocrit Suppose the centrifuge is just starting up, and that it has an angular speed of 8.00 rad/s and an angular acceleration of 95.0 rad/s2. (a) What is the magnitude of the centripetal, tangential, and total acceleration of the bottom of a tube? (b) What angle does the total acceleration make with the direction of motion?

More Related