P2F11-Week9-Barwick

P2F11-Week9-Barwick - P2 Week 9 Rotational motion and...

Info icon This preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
P2 Week 9 Rotational motion and kinematic equations Reading: Sec 3.4
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rigid Object A rigid object is one that is nondeformable The relative locations of all particles making up the object remain constant All real objects are deformable to some extent, but the rigid object model is very useful in many situations where the deformation is negligible
Image of page 2
Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Angular Position, 2 Point P will rotate about the origin in a circle of radius r Every particle on the disc undergoes circular motion about the origin, O Polar coordinates are convenient to use to represent the position of P (or any other point) P is located at ( r , θ ) where r is the distance from the origin to P and θ is the measured counterclockwise from the reference line
Image of page 4
Angular Position, 3 As the particle moves, the only coordinate that changes is θ As the particle moves through θ , it moves though an arc length s . The arc length and r are related: s = θ r compare to calculation of s in cartesian coord.!
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Radian This can also be expressed as θ is a pure number, but commonly is given the artificial unit, radian One radian is the angle subtended by an arc length equal to the radius of the arc
Image of page 6
Conversions Comparing degrees and radians 1 rad = = 57.3° Converting from degrees to radians θ [rad] = θ [degrees] " 180 !
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Angular Position, final We can associate the angle θ with the entire rigid object as well as with an individual particle Remember every particle on the object rotates through the same angle The angular position of the rigid object is the angle θ between the reference line on the object and the fixed reference line in space The fixed reference line in space is often the x - axis
Image of page 8
Angular Displacement The angular displacement is defined as the angle the object rotates through during some time interval This is the angle that the reference line of length r sweeps out
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Average Angular Speed The average angular speed, ω , of a rotating rigid object is the ratio of the angular displacement to the time interval " av # z = $ 2 # $ 1 t 2 # t 1 = % $ % t Text Notation (Eqn 9.2) Alternate Notation
Image of page 10
Instantaneous Angular Speed The instantaneous angular speed is defined as the limit of the average speed as the time interval approaches zero
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Angular Speed Units of angular speed are radians/sec rad/s or s -1 Angular speed will be positive if θ is increasing (counterclockwise) Angular speed will be negative if θ is decreasing (clockwise)
Image of page 12
Directions, details Strictly speaking, the speed and acceleration ( ω , α ) are the magnitudes of the velocity and acceleration vectors, which point along the rotation axis The directions are actually given by the right-hand rule
Image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Angular Speed, final Because a rotating object often returns to its initial orientation, the time to complete one revolution is a convenient measure.
Image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern