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

[bruvvers]

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?

 

[kushan]

The acceleration you are calculating is centripetal acceleration . :O

 

[voko]

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.

 

[tiny-tim]

welcome to pf!

hi bruvvers! welcome to pf!

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

∴ 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

(and your arithmetic isn't correct anyway )

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!

… 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 ​

 

[Nickie]

Hi there,

It looks like you're on the right track with your second answer! The only thing that may be causing some confusion is the units you are using. Remember, angular velocity is measured in radians per second (rad/s) and angular acceleration is measured in radians per second squared (rad/s^2). Your calculation for angular velocity is correct, but for angular acceleration, you will need to divide by the time (3 seconds) to get the correct units. So the final answer for angular acceleration would be 177.32 rad/s^2.

Also, just a quick tip - when solving problems involving circular motion, it's always a good idea to double check your units and make sure they make sense. In this case, your units for angular acceleration should match the units of linear acceleration (m/s^2) since they are both measures of how quickly the object is changing its velocity.

I hope this helps! Keep up the good work.