Calculate Velocity of C Rotating About A Axis

  • #1

Homework Statement

[tex]A = (1,1,-2)[/tex]
[tex]C = (0,1,-5)[/tex]
(in cartesian coordinates)
Let A and C be drawn from a common origin and let C rotate about A with an angular velocity of 2 rad/s. Find the velocity of the head of C.

Homework Equations

[tex]v = w x r[/tex]

The Attempt at a Solution

w = 2 rad/s
I know I have to take the cross product of w and C (w x C = v) but I am having problems making w as a vector. Initially I thought I would use cylindrical coords and say that it's moving in the phi direction, unfortunately I don't know if that assumption is correct.
Can anyone give me a pointer on how I should begin to write w as a vector?
  • #2
If by w you mean [itex]\omega[/itex], the angular velocity, then the direction of omega is always perpendicular on the plane of the speed v. Use the right-hand-rule: If you curl your fingers in the direction of v, then the thumb (stretched out) is the direction of omega.

For example, the direction of omega for the hands of a clock (assuming they move with constant speed instead of in little jumps) would be into the clock.
  • #3
Omega points along the axis of rotation. It makes sense if you think about what the cross product does and the relation between omega, r and v.

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