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

AI Thread Summary
The discussion focuses on calculating angular velocity and acceleration for a rotating object, specifically a 2kg mass in a 1.5m radius circle over 3 seconds. Participants clarify the distinction between angular and linear measurements, emphasizing that centripetal acceleration is not the same as angular acceleration. The initial calculations presented were incorrect, particularly in applying the formulas for angular acceleration and velocity. To accurately compute these values, it's essential to determine if the object rotates at a constant speed or accelerates uniformly. Understanding these concepts is crucial for solving the problem correctly.
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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