Day 5 May 25 2009 study plan

3.9 Change of frame

Ex. 3.10, 3.11

WOE 16,17, 18

Points to Note

The main theme of the section is expressing velocity w.r.t. one Frame into velocity w.r.t. to a different frame

If XOY is one frame called S and X'O'Y' is another frame called S' we can express velocity of a body B w.r.t. S as a combination of velocity of body w.r.t. to S' and velocity of S' w.r.t to S.

**V**(B,S) =

**V**(B,S')+

**V**(S',S)

Where

**V**(B,S) = velocity of body w.r.t to S

**V**(B,S') = velocity of body w.r.t to S'

**V**(S',S) = velocity of S' w.r.t to S

we can rewrite above equation as

**V**(B,S') =

**V**(B,S)-

**V**(S',S)

We can interpret the above equation in terms of two bodies. Assume S', and B are two bodies. If we know velocities of two bodies with respect to a common frame (in this case S)we can find the velocity of one body with respect to the other body (V(B,S')

The above expressions for velocity were derived from the relation between position vectors of the body w.r.t. to S and S' and position vector of origin of S' with respect to origin of S.

**r**(B,S) =

**r**(B,S')+

**r**(S',S)

Differentiating the position vectors with respect to gives respective velocity

Formulas covered in the session

26.

**r**(B,S) =

**r**(B,S')+

**r**(S',S)

Where

**r**(B,S) = Position vector

**r**(B,S') = Position vector

**r**(S',S) = Position vector

27.

**V**(B,S) =

**V**(B,S')+

**V**(S',S)

Where

**V**(B,S) = velocity of body wrt to S)

**V**(B,S') = velocity of body wrt to S')

**V**(S',S) = velocity of S' wrt to S)

we can rewrite above equation as

28.

**V**(B,S') =

**V**(B,S)-

**V**(S',S)

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