Calculating Angular Velocity at the End of a Time Interval

In summary, angular velocity is a measure of the rate at which an object rotates around a fixed axis, usually measured in radians per second or degrees per second. It is calculated by dividing the change in angle by the change in time, or by multiplying the angular speed by the radius of rotation. Angular velocity differs from linear velocity as it measures rotational speed, while linear velocity measures straight line speed. It affects an object's motion by determining its rotational speed and centripetal acceleration. Some real-world applications include calculating the rotational speed of machines, determining vehicle orientation, and measuring celestial body rotation in astronomy.
  • #1
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Homework Statement


A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.165 revolutions during a 2.0 s time interval. What is the angular velocity at the end of this time interval?


Homework Equations


I was using the kinematic Equations
[itex]\theta[/itex]f = [itex]\theta[/itex]i + [itex]\omega[/itex]it + 0.5[itex]\alpha[/itex]t2

Am i doing something wrong?
The answers that I can choose are, 9.7 rad/s, 9.1 rad/s, 9.3 rad/s, 9.5 rad/s, 8.8 rad/s

All the answers I get are way larger

I must be doing something obviously wrong but I just can't see it.
 
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  • #2
Lets see your work then.
 

1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates around a fixed axis. It is usually measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angle (in radians or degrees) by the change in time. It can also be calculated by multiplying the angular speed (in radians or degrees per second) by the radius of the rotation.

3. What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of the rotational speed of an object around a fixed axis, while linear velocity is a measure of the speed of an object moving in a straight line. Angular velocity is measured in units of angles per time, while linear velocity is measured in units of distance per time.

4. How does angular velocity affect an object's motion?

The angular velocity of an object determines how quickly it rotates around a fixed axis. It also affects the object's centripetal acceleration, which is the acceleration towards the center of the rotation. A higher angular velocity will result in a faster rotation and a higher centripetal acceleration.

5. What are some real-world applications of angular velocity?

Angular velocity is used in many fields, including physics, engineering, and astronomy. It is used to calculate the rotational speed of machines, such as engines and turbines, and is also used in navigation systems to determine the orientation of vehicles. In astronomy, it is used to measure the rotational speed of celestial bodies and determine their shape and composition.

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