How Do You Calculate Angular Velocity and Acceleration for Rotating Objects?

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Homework Help Overview

The discussion revolves around calculating angular velocity and angular acceleration for a rotating object, specifically a 2kg mass rotating in a circle with a radius of 1.5m over a time period of 3 seconds. Participants are exploring the distinctions between angular and linear measurements, as well as the implications of centripetal acceleration versus angular acceleration.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to calculate angular velocity and acceleration but expresses confusion regarding their initial calculations and the definitions involved. Some participants question the assumptions made about the nature of the rotation, such as whether it is at a constant speed or involves acceleration from rest.

Discussion Status

Participants are actively engaging with the original poster's calculations, offering clarifications about the differences between angular and linear quantities. There is a recognition of potential confusion regarding the formulas used and the conditions of the problem, but no consensus has been reached on the correct approach or interpretation.

Contextual Notes

There is a lack of clarity regarding whether the object is rotating at a constant speed or starting from rest, which affects the calculation of angular acceleration. Additionally, the original poster's calculations have been noted as potentially incorrect, but specific errors have not been resolved.

bruvvers
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Hi guys,

I'm stumped on just one question and not sure where to go with it now. Any help would be greatly appreciated...

Question:
Calculate the angular acceleration and angular velocity of a 2kg object rotating in a circle of 1.5m radius in a time of 3s.

My first answer i realize now was wrong due to calculating linear velocity

Second answer:

ω=3*(2∏)2=6∏ rad/s

∴ α=ω2r=(6∏)2*1.5=532.96 rad/s2

Can anyone offer some assistance on where I'm going wrong here please?
 
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The acceleration you are calculating is centripetal acceleration . :O
 
To compute the angular velocity, all you need is the period of on rotation. It does not depend on the radius, nor does it depend on the mass.

To compute the angular acceleration, you need to know how angular velocity changes. The problem has no data on this.
 
welcome to pf!

hi bruvvers! welcome to pf! :smile:

hmm … you're obviously completely confused about the difference between angular and linear measurements, and between angular acceleration and centripetal acceleration

bruvvers said:
∴ α=ω2r=(6∏)2*1.5=532.96 rad/s2

ω2r (= v2/r) is the formula for centripetal acceleration

centripetal acceleration is simply the component of linear acceleration in the (negative) radial direction

centripetal acceleration is measured in m/s2​

centripetal acceleration has nothing to do with angular acceleration!

angular acceleration is measured in rad/s2​
ω=3*(2∏)2=6∏ rad/s

i'm not sure what you've done here :confused:

(and your arithmetic isn't correct anyway :redface:)

the question is …
Calculate the angular acceleration and angular velocity of a 2kg object rotating in a circle of 1.5m radius in a time of 3s.

… does this mean that it is rotating at a constant angular speed? if so, the angular acceleration is obviously zero! :rolleyes:

… or does it mean that it starts from rest, accelerates uniformly, and completes its first circle in 3s ? if so, use the standard constant acceleration formulas, adapted for constant angular acceleration

show us what you get :smile:​
 

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