# Relative velocity and acceleration on rotating axis

• azula.ozai
In summary, the conversation discusses the problem of finding the relative and absolute velocity and acceleration of a package on a conveyor belt. The conveyor belt is rotating about a pivot point at an angular velocity of 6 rad/s, and also has a constant linear velocity of 1.5 m/s. The package is located 1.8 m away from the origin, and the conveyor belt is at a 45 degree angle from the horizontal y-axis. The difficulty lies in determining which formula to use to solve the problem.
azula.ozai

## Homework Statement

given a package on a conveyor belt running at a constant veloctiy of 1.5m/s, 1.8m away from the origin. the conveyor belt is rotating origin as a pivot at angular velocity 6 rad/s. it rotates on z axis. calculate the relative velocity of the package from origin (Vp/0) and V absolute. calculate also the relative acceleration (A p/0) and absolute accelearation

## Homework Equations

Vp = Vo + Vp/o...<---Vo = 0 since origin, thus Vp/0 = Vp..
Vp = Vo + (w x r)...(angular velocity x distance)..(but angular velocity of conveyor belt is not given)..
what is absolute velocity

## The Attempt at a Solution

usually i use the formula Vp = w x r (angular velocity cross product r (distance)

i am confused of how and which formula to use to solve this question. please help me

Hi azula.ozai, welcome to Physics Forums.

It's not entirely clear (to me ) from the description what the conveyor belt geometry is. Is it a planar ring-shaped belt circling the origin (sort of like a turning Compact Disk)?

oh sorry gneill...it's like the conveyor belt in the airport. or in the grocery counter..but is rotate about point 'o' on z axis (weird..but yeah). it's 45 degree above horizontal y axis. sorry I'm not able to attach the question here. and at the same time the belt moves with contant v of 1.5 m/s. the pacakge on the conv. belt is 1.8m away from origin. so it's going to have it's z and y component.

azula.ozai said:
oh sorry gneill...it's like the conveyor belt in the airport. or in the grocery counter..but is rotate about point 'o' on z axis (weird..but yeah). it's 45 degree above horizontal y axis. sorry I'm not able to attach the question here. and at the same time the belt moves with contant v of 1.5 m/s. the pacakge on the conv. belt is 1.8m away from origin. so it's going to have it's z and y component.

So the conveyor is something like the one depicted in the attached figure, only it's overhead view would be circular?

#### Attachments

• Fig3.gif
12.3 KB · Views: 533

I would suggest starting by clearly identifying and defining the variables in the problem. In this case, we have a package on a conveyor belt moving at a constant velocity, with the conveyor belt rotating at a given angular velocity. The package is located 1.8m away from the origin, which is also the axis of rotation.

Next, we can consider the relative velocity of the package from the origin (Vp/0). This will be the sum of the package's velocity relative to the conveyor belt (Vp/belt) and the conveyor belt's velocity relative to the origin (Vbelt/0). Since the conveyor belt is rotating with a constant angular velocity, we can use the formula Vbelt/0 = w x r, where w is the angular velocity and r is the distance from the origin to the package (1.8m in this case). Therefore, Vp/0 = Vp/belt + w x r.

To find the absolute velocity (Vp), we simply need to add the velocity of the conveyor belt (Vbelt) to the relative velocity of the package from the origin (Vp/0). Since the conveyor belt is moving at a constant velocity, we can use the formula Vbelt = Vbelt/0 = w x r.

To calculate the relative acceleration (Ap/0), we can use the formula Ap/0 = Arel + (w x Vp), where Arel is the relative acceleration of the package on the conveyor belt (which is simply 0 since the package is moving at a constant velocity on the belt) and w x Vp is the Coriolis acceleration due to the rotation of the conveyor belt. This can be calculated using the formula w x Vp = w x (w x r), where w is the angular velocity of the conveyor belt and r is the distance from the origin to the package.

Finally, the absolute acceleration (Ap) can be found by adding the acceleration of the conveyor belt (Abelt) to the relative acceleration of the package from the origin (Ap/0). Since the conveyor belt is rotating at a constant angular velocity, we can use the formula Abelt = (w x Vbelt) + (w x w x r).

I hope this helps clarify the problem and provides a starting point for solving it. Remember to always carefully define your variables and use appropriate formulas and equations to solve the problem.

## 1. How is relative velocity defined on a rotating axis?

Relative velocity on a rotating axis is the velocity of an object in relation to another object on a rotating axis. It takes into account both the linear velocity and the rotational velocity of an object.

## 2. What is the difference between absolute and relative velocity on a rotating axis?

Absolute velocity on a rotating axis is the velocity of an object in reference to a fixed point in space, while relative velocity takes into account the rotation of the axis and the velocity of another object on that axis.

## 3. How does angular velocity affect relative velocity on a rotating axis?

Angular velocity, or the rate of change of the angle of rotation, affects the relative velocity on a rotating axis by changing the direction and magnitude of the velocity vector. This is because the direction and magnitude of the linear velocity is dependent on the rotational velocity of the axis.

## 4. Can relative acceleration occur on a rotating axis?

Yes, relative acceleration can occur on a rotating axis. This is because acceleration is the rate of change of velocity, and on a rotating axis, both the linear and rotational velocities can change, causing a change in the relative velocity and thus, relative acceleration.

## 5. How does the Coriolis effect relate to relative velocity and acceleration on a rotating axis?

The Coriolis effect is a result of the Earth's rotation and causes the deflection of objects from a straight path. It is related to relative velocity and acceleration on a rotating axis because it affects the direction of the velocity and acceleration vectors, making them appear to curve or rotate. This effect is important in understanding the movement of objects on a rotating axis, such as in weather patterns or the trajectory of projectiles.

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