Relative angular velocity in a rotating rod

In summary, we discussed a rod rotating about one end with a constant angular velocity. We then looked at finding the relative angular velocity of the end B with respect to the midpoint of the rod using two different methods. The first method involves directly subtracting the angular velocities, while the second method involves finding the velocities of each point and then calculating the relative velocity. Both methods give the same result, but it is important to choose the appropriate frame of reference when analyzing rotational motion.
  • #1
TyrionTestBok
3
0
Consider a rod AB rotating about one of it's end A with angular velocity w.
Now angular velocity of each point of the rod is same i.e. w.
But if we have to find the relative angular velocity of the end B w.r.t. mid point of rod, what it will be?

Will it be zero because, w-w=0

or first we have to find the velocity of end B which is wR(R is length of Rod)
then find velocity of mid-point wR/2 and then find relative velocity of end B w.r.t. to mid point which is
wR-wR/2=wR/2
then divide it by distance between B and mid point which is R/2 and get relative angular velocity which now comes out to be w.

Which method is right and why the other method is wrong?
 
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  • #2
TyrionTestBok said:
Now angular velocity of each point of the rod is same i.e. w.
You seem to have answered your own question.
 
  • #3
Svein said:
You seem to have answered your own question.
But why two answer are coming through different method?
 
  • #4
Make your xy coordinates at the end that is stationary. Clearly, as you say, the other end is rotating in that frame of reference.

Now make your xy coordinates with the x-axis along the rod and the y-axis perpendicular to that. Are any points on the rod rotating in that frame of reference?
 
  • #5
phinds said:
Make your xy coordinates at the end that is stationary. Clearly, as you say, the other end is rotating in that frame of reference.

Now make your xy coordinates with the x-axis along the rod and the y-axis perpendicular to that. Are any points on the rod rotating in that frame of reference?
I didnt get you. Sorry :(
 

FAQ: Relative angular velocity in a rotating rod

What is relative angular velocity?

Relative angular velocity refers to the rate at which an object rotates relative to another object. It is a measure of how fast the angle between the two objects is changing.

How is relative angular velocity calculated?

Relative angular velocity is calculated by dividing the difference in angular position of two objects by the time it takes for the change to occur. This can be represented by the equation: ω = ∆θ/∆t, where ω is the relative angular velocity, ∆θ is the change in angular position, and ∆t is the change in time.

What factors affect relative angular velocity?

The relative angular velocity of two objects can be affected by various factors, such as the distance between the objects, the mass of the objects, and the speed at which the objects are rotating. Additionally, the presence of external forces or friction can also impact the relative angular velocity.

How is relative angular velocity different from linear velocity?

Relative angular velocity measures the rotational speed of an object, while linear velocity measures the speed at which an object moves in a straight line. While relative angular velocity is measured in radians per second, linear velocity is measured in meters per second.

What is the importance of studying relative angular velocity?

Studying relative angular velocity is important in understanding the motion of objects in a rotating system. It is particularly relevant in engineering and physics, as it can help in designing and analyzing mechanisms, such as gears and pulleys, that involve rotational motion. It also has applications in fields such as astronomy, where the relative angular velocity between celestial bodies can provide information about their movements and interactions.

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