03032009 - Kinematics Motion of a Particle A reference...

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

View Full Document Right Arrow Icon
Kinematics – Motion of a Particle A reference frame is a coordinate system specifying the positions of points by specifying the components of the position vector r relative to the origin. Suppose P is in a motion relative to the chosen reference frame, so the r is a function of time t r = r(t ) describes the motion of P
Image of page 1

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

View Full Document Right Arrow Icon
Velocity of Particle in Motion The velocity of P relative to the given reference frame at time t is defined by ) 1 . 13 ( ) ( r ) ( r lim r v 0 t t t t dt d t Δ Δ + = = Δ where the vector r(t+ Δ t) – r(t) is the change in position, or displacement, of P during the interval of time Δ t Therefore, the velocity v is the rate of change of position of P.
Image of page 2
Acceleration of Particle in Motion The acceleration of P relative to the given reference frame at time t is defined by ) 2 . 13 ( ) ( v ) ( v lim v a 0 t t t t dt d t Δ Δ + = = Δ where v(t+ Δ t) – v(t) is the change in velocity of P during the interval of time Δ t . Acceleration is the rate of change of the velocity of P at time t i.e. ) / ( r r 2 2 2 s m dt d or dt d dt d
Image of page 3

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

View Full Document Right Arrow Icon
Reference Frame for Motion of Particle Let O’ be an arbitrary fixed point and r’ be the position vector from O’ to P dt d ' r ' v = Velocity of P relative to O’ is Velocity of P relative to O is dt d r v = dt d ' r ' v =
Image of page 4
Reference Frame for Motion of Particle v r R r ' r ' v = = = = dt d dt d dt d dt d Let R be the vector from O to O’ such that r = R + r’ or r’ = r – R R is a constant, therefore, velocity of P relative to O’ is Similarly, for acceleration dt d and dt d v a ' v ' a = = Therefore, v’ = v and a’ = a Î The velocity and acceleration of a point P relative to a given frame of reference do not depend on the location of the fixed reference point used to specify the position of P.
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