How Does the Cross Product Determine the Perpendicularity of Angular Velocity?

In summary, the direction of angular velocity is determined by the right-hand rule and is always perpendicular to the plane of rotation. It can be negative and affects the motion of an object by determining its angular momentum. The object's mass does not affect the direction of angular velocity, but it can impact its angular momentum.
  • #1
Miraj Kayastha
80
0
V = ωr

V= velocity
ω = angular velocity
r = radius

How is the direction of ω perpendicular to the plane of rotation?

Is the formula ω = vsinθ χ 1/r which is the cross product of vsinθ and 1/r the reason why ω is perpendicular to the plane of rotation?
 
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  • #2
ω is perpendicular to the plane of rotation because it is parallel with the axis of rotation.
 
  • #3
ω = (r x v)/|r|2
 

FAQ: How Does the Cross Product Determine the Perpendicularity of Angular Velocity?

What is the direction of angular velocity?

The direction of angular velocity is determined by the right-hand rule. If you curl the fingers of your right hand in the direction of rotation, then your thumb will point in the direction of angular velocity.

How is the direction of angular velocity related to the direction of rotation?

The direction of angular velocity is always perpendicular to the plane of rotation. This means that the direction of angular velocity will change as the direction of rotation changes.

Can the direction of angular velocity be negative?

Yes, the direction of angular velocity can be negative. Negative angular velocity indicates rotation in the opposite direction, or clockwise rotation, while positive angular velocity represents counterclockwise rotation.

How does the direction of angular velocity affect the motion of an object?

The direction of angular velocity determines the direction of the object's angular momentum, which is the tendency of an object to continue rotating in a particular direction. A change in the direction of angular velocity can result in a change in the direction of angular momentum and therefore alter the object's motion.

Is the direction of angular velocity affected by the object's mass?

No, the direction of angular velocity is not affected by an object's mass. It is solely dependent on the direction and speed of rotation. However, the object's mass can affect its angular momentum, which is related to angular velocity.

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