# Angular Velocity and Acceleration graph

• df102015
In summary, the conversation discusses finding the angular displacement and acceleration from a given graph. The equations used include α = at/r, α = ω/t, α = Θ/t^2, ω = Θ/t, ω = v/r, and Θ = ωt + 0.5αt^2. There is an error in the image provided. The correct approach for finding the distance moved from a velocity-time graph is aavg=Δv/Δt. The angular acceleration is constant in the given scenario.
df102015

## Homework Statement

A.) For the graph above what is the angular displacement during the 4 seconds of motion?
B.) For the graph above what is the angular acceleration from t=2 to t=4?

## Homework Equations

α = at / r
α = ω / t
α = Θ / t^2
ω = Θ / t
ω = v / r
Θ = ω t + 0.5 α t^2

## The Attempt at a Solution

A.) I used ω = Θ / t
rearranged it to ωt = Θ

but my issue is what ω do i use? 0, 10, 20? anything in between? And is this even the right equation to use?

B.) Isn't it not accelerating between t2 and t4? Or is it constant acceleration?
How i went about it is i used α = ω / t
since the time is 2 seconds, and the ω is 20. i got 10, but that was wrong :(

There is an error in your image, unfortunately.

ProfuselyQuarky said:
There is an error in your image, unfortunately.
fixed it

For the first part it is the area under the graph.
For the second part the angular acceleration is constant.

df102015 said:
what ω do i use?
Do you know how to find the distance moved from a velocity-time graph?
df102015 said:
α = ω / t
Quoting formulae is of little use unless you know what the terms in the formulae represent. E.g. a=v/t is more informatively written as aavg=Δv/Δt. I.e. the average acceleration is the increase in velocity divided by the elapsed time.
kinemath said:
For the second part the angular acceleration is constant
True, but of the choice
df102015 said:
not accelerating between t2 and t4? Or is it constant acceleration?
@df102015 , what do you look at on a velocity-time graph to deduce the acceleration?

## 1. What is Angular Velocity?

Angular velocity is the rate of change of angular displacement with respect to time. It is a measure of how quickly an object is rotating around an axis.

## 2. How is Angular Velocity calculated?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. The units for angular velocity are radians per second (rad/s) or degrees per second (deg/s).

## 3. What is an Angular Velocity and Acceleration graph?

An Angular Velocity and Acceleration graph is a visual representation of the relationship between angular velocity and angular acceleration over time. It plots the change in angular velocity on the y-axis and the change in time on the x-axis.

## 4. What can be learned from an Angular Velocity and Acceleration graph?

An Angular Velocity and Acceleration graph can provide information about the rotation of an object, such as its direction and speed. It can also indicate any changes in the angular velocity or acceleration over time, which can help understand the motion of the object.

## 5. How is Angular Velocity related to Angular Acceleration?

Angular velocity and angular acceleration are related by the equation ω = αt + ω0, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time. This equation shows that the angular velocity changes proportionally to the angular acceleration and time.

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