Rotational motion (confused about the variables)

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Homework Help Overview

The discussion revolves around the concepts of rotational motion, specifically focusing on various types of acceleration such as linear, centripetal, tangential, angular acceleration, and their interrelations. Participants are exploring the definitions and differences between these accelerations in the context of circular motion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the distinctions between centripetal acceleration and angular acceleration, questioning whether they measure the same phenomenon. There are discussions about the implications of constant speed on these accelerations and the relationship between angular speed and angular velocity.

Discussion Status

The discussion is active, with participants providing insights and clarifications regarding the definitions of different types of acceleration. Some participants express confusion about the relationships between these concepts, while others offer explanations that help to clarify the distinctions. There is no explicit consensus yet, but productive dialogue is ongoing.

Contextual Notes

Participants are navigating through the complexities of rotational motion, including the implications of dimensionality on angular velocity and acceleration. The discussion reflects a learning environment where assumptions and definitions are being critically examined.

madah12
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we have many accelerations in rotational motion ,and I don't know the difference between them. first the linear acceleration which as I understand is the vector acceleration which has the same direction as the change of velocity and it affects the speed and direction then it's two components are centripetal acceleration which changes the angle and is towards the center and it doesn't change the magnitue of the velocity. Then there is the tangential acceleration which is perpendicular to the centripetal acceleration and it increases the magnitude of the velocity.
First is my understanding of the acceleration correct ? second I also see that we have the angular acceleration and it changes the the the angular velocity but this confuses me what is the difference between it and the centripetal acceleration? they both change the angle.
 
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Here's how I'd put it. Something moving in a circle has a linear (or translational) acceleration. That acceleration has two components: a centripetal component and a tangential component.

What is usually called the angular acceleration is the rate of change of angular speed. The angular speed relates to the tangential speed via: ω = r*vt. In turn, the angular acceleration relates to the tangential acceleration via: α = r*at.

Does that help?
 
but what I don't understand is whether the centripetal acceleration and the angular acceleration are measuring the same thing or not? I mean they all affect the change of the direction of the velocity right?
 
madah12 said:
but what I don't understand is whether the centripetal acceleration and the angular acceleration are measuring the same thing or not?
No. Centripetal acceleration is the rate of change in linear velocity (for constant speed). Angular acceleration is the rate of change of the angular speed. For something moving with constant speed, there will be a non-zero centripetal acceleration while the angular acceleration will be zero.
 
Doc Al said:
No. Centripetal acceleration is the rate of change in linear velocity (for constant speed). Angular acceleration is the rate of change of the angular speed. For something moving with constant speed, there will be a non-zero centripetal acceleration while the angular acceleration will be zero.

oh thanks I see it now but if angular acceleration is the rate of change of angular speed then what is the rate of change of angular velocity?
 
madah12 said:
oh thanks I see it now but if angular acceleration is the rate of change of angular speed then what is the rate of change of angular velocity?
As long as the axis of rotation doesn't change, as when you stick to two dimensions, angular speed and velocity are the same (for practical purposes). When you deal in three dimensions, and the axis of rotation can change, things get complicated fast. Angular velocity is a vector (pseudovector, really) whose magnitude is the angular speed and whose direction is along the axis of rotation. See: http://en.wikipedia.org/wiki/Angular_velocity"
 
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but isn't the rotation negative if it is clockwise?
 
madah12 said:
but isn't the rotation negative if it is clockwise?
That's the convention, sure.
 

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