Angular acceleration and angular velocity

AI Thread Summary
The discussion focuses on calculating the angular acceleration and angular velocity of a 4 kg object rotating in a circle with a radius of 3 m over 6 seconds. It highlights that the initial attempt at calculating angular acceleration using the formula ω²*r is incorrect, as this represents centripetal acceleration and is dimensionally inconsistent. The correct interpretation is that without information on how angular velocity changes over time, angular acceleration is assumed to be zero. The formula for angular velocity, defined as angular displacement divided by time, is confirmed to be valid. Overall, the key takeaway is that angular acceleration is zero while the method for calculating angular velocity is acceptable.
John78
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Homework Statement



Calculate the angular acceleration and angular velocity of a 4 kg object rotating in a circle of 3 m radius in a time of 6 s.

Homework Equations





The Attempt at a Solution



Angular acceleration = ω2*r

C=2∏r= 2*3.14*3=18.84
360°/57.3°=6.28 rad/s
6.28/6= 2.09 rad/sec

Angular acceleration= (2.09)2*3=12.54??


Angular velocity= angular displacement/time ?



I just want to check whether my working is correct or not.
 
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Nope.Its not right.

Remember, angular acceleration is dw/dt.

The acceleration w^2*r is centripetal accelwration.

Infact writing angular acceleration as w^2*r is dimemsionally inconsistent.


As nothing had been told about how w changes with time nothing can be said about angular acceleration.

In such cases w is assumed to be constant making angular acceleration 0
 
angular acceleration = 0


what about angular velocity?
 
Hi John78! :smile:
John78 said:
angular acceleration = 0

Correct.
what about angular velocity?

Your formula …
Angular velocity= angular displacement/time
… is fine :smile:
 

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