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

Info iconThis 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
Background image of page 1

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

View Full DocumentRight 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.
Background 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
Background image of page 3

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

View Full DocumentRight 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 =
Background 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.
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/28/2010 for the course CIVIL CIVL1010 taught by Professor Unknown during the Spring '09 term at HKU.

Page1 / 18

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online