Relative velocity and acceleration on rotating axis

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Discussion Overview

The discussion revolves around calculating the relative and absolute velocity and acceleration of a package on a conveyor belt that rotates around a pivot point at a specified angular velocity. The scenario involves understanding the geometry of the conveyor belt and its motion in a three-dimensional space, particularly focusing on the z and y components of the motion.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • The initial problem statement includes a package on a conveyor belt moving at a constant velocity of 1.5 m/s, located 1.8 m from the origin, with the conveyor rotating about the z-axis at an angular velocity of 6 rad/s.
  • One participant expresses confusion regarding the appropriate formulas to use for calculating the relative velocity and acceleration, indicating uncertainty about the angular velocity of the conveyor belt.
  • Another participant seeks clarification on the geometry of the conveyor belt, asking if it resembles a planar ring-shaped belt or a different configuration.
  • A later reply clarifies that the conveyor belt is similar to those found in airports or grocery stores, rotating about a point on the z-axis and positioned at a 45-degree angle above the horizontal y-axis.
  • The same participant reiterates the motion of the conveyor belt and the position of the package, emphasizing the need to consider both z and y components in the calculations.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the conveyor belt's geometry or the correct approach to solve the problem. There is ongoing clarification and exploration of the scenario without a definitive resolution.

Contextual Notes

The discussion highlights potential limitations in understanding the conveyor belt's geometry and the implications for calculating relative and absolute velocities and accelerations. There are unresolved aspects regarding the application of the angular velocity in the context of the problem.

azula.ozai
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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
 
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Hi azula.ozai, welcome to Physics Forums.

It's not entirely clear (to me :smile:) 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

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