Angular acceleration and angular velocity

In summary, the conversation discusses calculating 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. The formula for angular acceleration is ω2*r, but this is dimensionally inconsistent. Without information on how ω changes with time, it is assumed to be constant and the angular acceleration is 0. The formula for angular velocity is angular displacement/time.
  • #1
John78
21
0

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.
 
Physics news on Phys.org
  • #2
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
 
  • #3
angular acceleration = 0


what about angular velocity?
 
  • #4
Hi John78! :smile:
John78 said:
angular acceleration = 0

Correct.
what about angular velocity?

Your formula …
Angular velocity= angular displacement/time
… is fine :smile:
 
  • #5


Yes, your working is correct. To find the angular velocity, you would use the formula ω=θ/t, where θ is the angular displacement (in radians) and t is the time. In this case, the angular displacement is 2.09 radians (converted from 360°), and the time is 6 seconds. Therefore, the angular velocity would be 2.09/6 = 0.35 rad/s.
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly an object's angular velocity is changing, either increasing or decreasing.

2. How is angular acceleration different from linear acceleration?

While linear acceleration measures the change in an object's linear velocity, angular acceleration measures the change in an object's angular velocity. Linear acceleration is measured in meters per second squared, while angular acceleration is measured in radians per second squared.

3. How is angular acceleration related to angular velocity?

Angular acceleration and angular velocity are directly related. An increase in angular acceleration will result in a corresponding increase in angular velocity, and vice versa. This relationship is described by the equation: angular acceleration = change in angular velocity / change in time.

4. How is angular velocity calculated?

Angular velocity can be calculated by dividing the change in angle by the change in time. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

5. How does angular acceleration affect rotational motion?

Angular acceleration is responsible for changing an object's rotational speed and direction. A positive angular acceleration will cause an object to rotate faster in a counterclockwise direction, while a negative angular acceleration will cause it to rotate slower or in a clockwise direction.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
709
  • Introductory Physics Homework Help
Replies
6
Views
874
  • Introductory Physics Homework Help
Replies
8
Views
919
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
325
  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
32
Views
975
  • Introductory Physics Homework Help
10
Replies
335
Views
7K
  • Introductory Physics Homework Help
Replies
12
Views
917
Back
Top