Angular Velocity Calculation

In summary, the conversation discusses the correct way to solve a problem involving rotational motion, specifically the relationship between linear and angular velocity. The formula v = w x r is used, but it is important to measure the distance from the center of rotation to the point of interest. This is due to the concept of similar triangles and the fact that v = 2r x w is the correct formula to use. The importance of measuring from the center of rotation is emphasized and clarified in the conversation.
  • #1
31
1

Homework Statement


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Homework Equations


v = w x r

The Attempt at a Solution


I got the answer correct after a few tries, but I am little confused on why it has to solved this specific way. I know that v = w x r, so why can I not just say w = v/r? Is it because w is measured from the center of the roller so v = w x r would be vcenter, not vtop?
That is how I ended up solving it, but I wanted to make sure I didn't get there "accidentally" or misinterpreted the process.
eCy96Ra.png

Using that diagram and concept of similar triangles:
tan θtop = tan θcenter
Stop/2r = Scenter/r
Stop = 2*Scenter, Scenter = rθ
Stop = 2rθ
d(Stop)/dt = vtop = d(2rθ)/dt = 2rθ' = 2rωtop
thus, ω = v/2r

Any reasoning as to why I have to do this would be much appreciated!
 
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  • #2
That's for the centro of the motion is at the bottom of the roller. Your formula should be applied as ##v=2r\cdot\omega,## where ##2r## is the distance from the bottom to the top.
 
  • #3
Ahh, i forgot, when using v = w x r you have to always measure from from IC unless using relative velocity equation. Thank you!
 

What is angular velocity and how is it calculated?

Angular velocity is a measure of an object's rotational speed around an axis. It is calculated by dividing the change in angular displacement by the change in time, typically measured in radians per second.

What is the difference between angular velocity and linear velocity?

Angular velocity measures the rate of change of angular displacement, while linear velocity measures the rate of change of linear displacement. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

What factors can affect the calculation of angular velocity?

The calculation of angular velocity can be affected by the radius of the object's rotation, the object's mass and shape, and the force acting upon the object.

How is angular velocity used in real-world applications?

Angular velocity is used in various fields such as physics, engineering, and astronomy. It is used to describe the motion and rotation of objects, and is essential in understanding and predicting the behavior of systems such as spinning tops, rotating engines, and celestial bodies.

Can angular velocity be negative?

Yes, angular velocity can be negative. A negative angular velocity indicates that the object is rotating in the opposite direction of the chosen direction of rotation. This can happen when the object is rotating clockwise instead of counterclockwise, or when there is a decrease in angular displacement over time.

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