# Quick question about centers of instantaneous velocities

• rdg29
In summary, when B is moving to the right at a speed of Vb and its position is located directly below the connection between B2 and B3, the instantaneous center of B2 will have a velocity of 0. This can tell us that the angular velocity of B3 is also 0, as the velocity at point A is restricted to be tangential to the circular path around C. As B2 becomes more vertical, the magnitude of the angular velocity of B3 decreases until it reaches a point of 0, as any point after this instant will have the angular velocity begin to change in the opposite direction. This analysis suggests that the angular velocity of B3 is in one direction before B2 becomes vertical and then changes direction

## Homework Statement

If at some time t, the position of B (the intersection between bodies B1 and B2) is located directly below the connection between bodies B2 and B3. B is moving to the right at a speed of Vb. What happens to the instantaneous center of B2, and what can this tell you about the angular velocity of B3? (Note: body B3 is pinned at the location C and B is restricted to move in the horizontal direction). Explain.

## Homework Equations

Velocity of the instant center is 0.
v = rw, where v = velocity, r = distance to the point, and w = angular velocity

## The Attempt at a Solution

Since the perpendicular path of the velocity of B passes through point A, and the velocity of A is restricted to be moving tangent to the circular path around C, the only thing that makes sense to me is if B3 has an angular velocity to be 0 and the velocity at A is zero. The reason why is because at any moment prior to the instant that B2 is vertical, the angular velocity of B3 has to be in one direction since theta is growing, but as the body becomes more and more vertical, the magnitude of this velocity decreases until it has to reach a zero point since any point following this instant will have the angular velocity begin to change in the opposite direction (theta will be getting smaller).

I am a little concerned that my reasoning here may be off though, or that I'm missing something important.

rdg29
mfb said:

Thanks for looking it over.

## 1. What is a center of instantaneous velocity?

A center of instantaneous velocity is a point on an object that represents the average location of all the instantaneous velocities of that object at a given instant in time. It is also known as the instantaneous center of rotation or instant center.

## 2. How is the center of instantaneous velocity calculated?

The center of instantaneous velocity can be calculated by finding the intersection point of two perpendicular lines that represent the instantaneous velocities of two points on the object. Alternatively, it can also be found by using the concept of instantaneous axis of rotation.

## 3. Why is the center of instantaneous velocity important in physics?

The center of instantaneous velocity is important because it helps to understand the motion of objects and their instantaneous velocities at a given moment in time. It is also used in the study of rotational motion and the relationship between linear and angular velocities.

## 4. Is the center of instantaneous velocity always constant?

No, the center of instantaneous velocity is not always constant. It changes as the object moves and its instantaneous velocities change. However, for an object with constant linear and angular velocities, the center of instantaneous velocity will also be constant.

## 5. How does the center of instantaneous velocity relate to the center of mass?

The center of instantaneous velocity and the center of mass are two different concepts. The center of mass is the average location of an object's mass, while the center of instantaneous velocity represents the average location of its instantaneous velocities. However, for rigid bodies, the center of mass and the center of instantaneous velocity will coincide.