Calculate Velocity of C Rotating About A Axis

In summary, the problem involves finding the velocity of the head of C, which is rotating about A with an angular velocity of 2 rad/s. The formula for velocity is v = w x r, where w is the angular velocity and r is the position vector. Using the right-hand-rule, the direction of w is perpendicular to the plane of v. Therefore, the direction of w for the rotating hands of a clock would be into the clock.
  • #1
jesuslovesu
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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?
 
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  • #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.
 

What is the formula for calculating the velocity of a point on a rotating object?

The formula for calculating the velocity of a point on a rotating object is v = rω, where v is the velocity, r is the distance from the point to the axis of rotation, and ω is the angular velocity.

How do you calculate the angular velocity of an object?

The formula for calculating angular velocity is ω = θ/t, where ω is the angular velocity, θ is the angular displacement, and t is the time it took to complete that displacement.

What is the difference between angular velocity and linear velocity?

Angular velocity is the rate of change of angular displacement, while linear velocity is the rate of change of linear displacement. In other words, angular velocity tells us how quickly an object is rotating, while linear velocity tells us how quickly an object is moving in a straight line.

How does calculating the velocity of a rotating object help in understanding its motion?

Calculating the velocity of a rotating object allows us to understand how fast the object is rotating and how that rotation affects its movement. It also helps us analyze the forces acting on the object and predict its future motion.

What factors can affect the velocity of a rotating object?

The velocity of a rotating object can be affected by factors such as the object's mass, distance from the axis of rotation, and the amount of torque applied to it. Changes in these factors can result in changes in the object's angular velocity and linear velocity.

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