# Angular Quantities: Calculating Revolutions

• catenn
In summary, the conversation discusses the relationship between angular quantities and revolutions, specifically in regards to finding the distance traveled by a tire. It is mentioned that the circumference of a circle can be found by multiplying the radius by 2 pi, and the distance traveled by a wheel is equal to the circumference times the number of rotations. The concept of relating angular displacement to linear displacement using trigonometry is also brought up.
catenn
Hey, I ran into a few things about angular quantites and am a little confused on finding the number of revolutions something such as a tire would make. Would the distance traveled divided by a circumference of a circle equal the number of revolutions? I was finding that there are equations that show an angular displacement divided by 2 pi, so if a radius is known is it useful or not? I couldn't decide whether to divide anything by a radius of Circumference or just 2 pi. Also, with angular displacement would it work to use just displacement in linear distances? Thanks!

To find the circumference, you times the radius by 2 pi.

Finding the distance a wheel covers is merely the circumference times by the number of revolutions. So a wheel with a radius of 30cm rotating 2.5 times will travel 471cm. Ok?

So the distance traveled by a wheel will equal the circumference * number of rotations.

You can relate angular displacement to linear displacement using trigenometry, are you familiar with this?

Thanks so much, that really helps! :)

## 1. What is the definition of "angular quantity"?

Angular quantity refers to a measurement of rotation, specifically the amount of rotation that has occurred around a particular axis or point. It is commonly measured in units such as degrees, radians, or revolutions.

## 2. How do you calculate the number of revolutions?

To calculate the number of revolutions, you need to know the total angular distance traveled and the size of one revolution. You can then divide the total distance by the size of one revolution to get the number of revolutions.

## 3. What is the relationship between angular quantities and linear quantities?

Angular quantities and linear quantities are related through the concept of arc length. The arc length is equal to the radius of rotation multiplied by the angular quantity (in radians). This means that a larger angular quantity will result in a longer arc length, while a smaller angular quantity will result in a shorter arc length.

## 4. How does angular velocity affect the number of revolutions?

Angular velocity is a measurement of how quickly an object is rotating. It is often measured in units such as radians per second or revolutions per minute. The higher the angular velocity, the more revolutions an object will complete in a given amount of time.

## 5. Can angular quantities be negative?

Yes, angular quantities can be negative. A negative angular quantity indicates rotation in the opposite direction from a positive angular quantity. For example, a positive 90 degrees would be a quarter turn to the right, while a negative 90 degrees would be a quarter turn to the left.

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