Lesson_4.1_Printable - Rotational Motion The figure on the...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Rotational Motion The figure on the right is a rotating disc. A is a point on the edge of the disc and O is its center. OA = r, the radius of the disc. The bunny sitting at A goes round as the disc rotates. A O B θ The bunny is initially at A and after a time t , it is at B OB the new position of the radius makes an angle θ with OA θ is called the angular displacement of the bunny in time t 1
Image of page 1

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

View Full Document Right Arrow Icon
A O B θ AB = r θ The rate of change of angular displacement of a rotating object is called is angular velocity ( ϖ ) ω = t θ ϖ is measured in radian per second Linear Speed and Angular Velocity The bunny traveled a linear distance equal to the length of the arc AB in time t . The linear speed v of the bunny is: arc AB v = t r = t θ = r t θ = r ϖ v = r ϖ 2
Image of page 2
A runner running at a constant pace gets halfway around a circular track that has a diameter of 500 m in 2.5 min. What are the runner’s (a) angular speed and (b) tangential speed? Radius of the track r = 500/2 = 250 m, t = 2.5 min = 150 s When the runner is halfway around the circle θ = π radians (b) v = r ϖ = 250 m × 0.021 rad.s -1 = 5.2 ms -1 -1 d radians (a) ω = dt 150 0.021 rad s .s θ π = = 3
Image of page 3

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

View Full Document Right Arrow Icon
The disc on the right has a radius 15 cm and it and it makes 12 revolutions every five seconds. (a) what is the angular velocity of the disc? (b) What is the linear speed of the bunny sitting at the edge of the disc? (a) The angle described by the disc for one revolution is 2 π radians. The angle described for 12 revolutions is: d ω = dt θ θ = 24 π radians -1 24 π radians = 5 4.8 rad s s π = t = 5 s 4
Image of page 4
The disc on the right has a radius 15 cm and it and it makes 12 revolutions every five seconds. (a) what is the angular velocity of the disc? (b) What is the linear speed of the bunny sitting at the edge of the disc?
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
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