# Finding angular velocity based on x vs t graph

• cuttooth
In summary, the conversation discusses a graph that appears to be representing Simple Harmonic Motion (SHM) and the problem asks for the angular velocity based on the given graph. The options given for angular velocity are 2.0 rad/s, 0.5 rad/s, 1 rad/sec, or none of the above. The conversation also mentions using the formula v(tangential) = ω r to determine the angular velocity, but there is some uncertainty about the accuracy of the graph.
cuttooth

## Homework Statement

I am given the attached graph (excuse my abysmal homemade graph!). On the y-axis, I presume that it is displacement (x). The x-axis is time. This graph looks like SHM, but I could be wrong! The graph rises from 0 to 2 every 2 seconds, and drops back to 0 on the y-axis for 2 seconds before repeating the cycle. The problem asks to find angular velocity based on the graph. I am given the choices of 2.0 rad/s, 0.5 rad/s, 1 rad/sec, or none of above.

## Homework Equations

This graph looks like SHM, but I could be wrong!

## The Attempt at a Solution

I really have no clue how to derive angular velocity based on this graph. I am guessing you have to find tangential velocity from the graph and from there determine angular velocity using the formula v(tangential) = ω r. Am I on the right track? Again, please excuse the poor graph. :)

#### Attachments

• unknown graph.jpg
10.8 KB · Views: 805
That graph can't be a x(t) plot because of the verticle segments. This says that somhow a particle covered some distance x in zero time. Also the velocity is undefined at those points. If you were just looking at it on a cycle or periodic basis then you would say it completes 1 cycle in 4s. And in one cycle there are 6.28rads. So you would get 1.57rad/s which would be none of the above.

I would first clarify the units of the y-axis to ensure that it is indeed displacement (x) and not something else. Then, I would plot the graph in a computer program or use a ruler to measure the data points and create a more accurate graph. From there, I would analyze the graph to determine if it is indeed simple harmonic motion (SHM) or not. If it is SHM, then I would use the equation x = A cos(ωt) to find the angular velocity (ω) by comparing the graph to this equation. If it is not SHM, then I would use other equations or methods to find the angular velocity. It is important to also consider the given choices and see if any of them match with the calculated angular velocity. If none of the choices match, then it is possible that the graph does not accurately represent the data or there may be an error in the calculations. Overall, it is important to thoroughly analyze the graph and use appropriate equations and methods to accurately determine the angular velocity.

## 1. How do you find angular velocity based on an x vs t graph?

To find angular velocity based on an x vs t graph, you need to first determine the slope of the graph. The slope represents the rate of change of angular displacement with respect to time. This rate of change is the angular velocity.

## 2. What is the formula for calculating angular velocity from an x vs t graph?

The formula for calculating angular velocity from an x vs t graph is ω = Δθ/Δt, where ω represents the angular velocity, Δθ represents the change in angular displacement, and Δt represents the change in time.

## 3. Can angular velocity be negative on an x vs t graph?

Yes, angular velocity can be negative on an x vs t graph. A negative angular velocity indicates that the object is rotating in the opposite direction of the chosen positive direction. This can occur if the object is slowing down or changing direction.

## 4. What are the units of angular velocity?

The units of angular velocity are radians per second (rad/s) in the SI system. However, it can also be expressed in revolutions per minute (RPM) or degrees per second (deg/s).

## 5. How is angular velocity related to linear velocity?

Angular velocity and linear velocity are related through the radius of rotation. The linear velocity of an object moving along a circular path is equal to the product of its angular velocity and the radius of the circle. This can be expressed as v = ωr, where v represents linear velocity, ω represents angular velocity, and r represents the radius of the circle.

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