# Angular velocity of a rolling object

• ZD_zainy
In summary, the conversation discusses the question about the behavior of a cylinder rolling down an incline. The person suggests considering extreme cases and discusses the differences between two possible answers. They also bring up the concept of torque and how it relates to the rotation of a rolling object. The conversation ends with a request to draw a diagram for a specific scenario to better understand the behavior of the cylinder.
ZD_zainy
Homework Statement
The question is in the attachment. I chose the 1st graph. But according to the scheme the correct one is the 3rd graph. I do not know what causes the sudden increase in the 3rd graph. Plz explain it
Relevant Equations
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#### Attachments

• 5529EEF2-DBDF-4835-91E9-8F24B0157634.jpeg
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Hello @ZD_zainy , !

Please read the PF guidelines: we are not allowed to help if you don't show your own attempt. What does one see in the graphs ?

It can help to consider extreme cases. What if the cylinder were already at the end of the slope when released?

BvU said:
Hello @ZD_zainy , !

Please read the PF guidelines: we are not allowed to help if you don't show your own attempt. What does one see in the graphs ?
How can I show my attempt which I made to find a graph?

haruspex said:
It can help to consider extreme cases. What if the cylinder were already at the end of the slope when released?
Oh sorry . The question’s diagram itself shows how the cylinder is in the slope

ZD_zainy said:
How can I show my attempt which I made to find a graph?
You write up what leads you to pick 1) and discuss the differences between 1) and 3). Where does it occur ?

Personally, I think the increase in ##\omega## is exaggerated (it looks almost like a jump)

For the angular velocity to exhibit a sudden increase at the very end when it flies off the incline, there must be an increased torque acting on it. Remember that a rolling object rotates about the instantaneous point of contact. What happens when it reaches the edge just before contact is lost?

ZD_zainy said:
Oh sorry . The question’s diagram itself shows how the cylinder is in the slope
You miss my point.
You are puzzled that the correct answer shows a sudden acceleration just as the cylinder reaches the end of the slope. The reason may become clear if you consider the cylinder released from rest when it is already touching the end of the slope.
Draw the diagram for that.

etotheipi

## 1. What is angular velocity?

Angular velocity refers to the rate of change of the angular position of a rolling object with respect to time. It is a measure of how fast the object is rotating.

## 2. How is angular velocity different from linear velocity?

Angular velocity is a measure of how fast an object is rotating, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity takes into account the object's distance from the axis of rotation, while linear velocity does not.

## 3. How is angular velocity calculated?

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

## 4. What factors affect the angular velocity of a rolling object?

The angular velocity of a rolling object is affected by the object's moment of inertia, the applied torque, and any external forces acting on the object. The surface on which the object is rolling and any frictional forces can also affect the angular velocity.

## 5. Can the angular velocity of a rolling object change?

Yes, the angular velocity of a rolling object can change if there is a change in the applied torque or external forces acting on the object. It can also change if the object's moment of inertia changes, such as when the object's shape or mass distribution changes.

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