# Angular and Linear Motion problem

• stf
In summary, the conversation discussed the problem of determining the angular velocity of a nail in radians per hour when it is lodged in a tire tread 13 inches from the center of the wheel and the car is moving at 55 miles per hour. The circumference of the circle made by the nail was calculated and used to determine the number of revolutions made in an hour. The conversation also briefly touched on the use of the imperial system and the simplicity of the solution.
stf

## Homework Statement

Automobile Tire: If a car runs over a nail at 55 mi/hr and the nail is lodged in the tire tread 13 in. from the center of the wheel, then what is the angular velocity of the nail in radians per hour?

w = alpha/time

a = s / r

## The Attempt at a Solution

I am not really sure where to start on this, obviously 13 in. is the radius, but I am unsure of how to get the angle alpha without a sector length. I assume it has something to do with the given 55 mph but don't see where it goes in.

If it is lodged 13 inches from the centre of the tyre, then what is the circumference of the circle it makes around it?

p.s. there's no way I'm going to help with the units of that flawed imperial system.
x inches = 1 mile, where x is some crazy and unnecessarily complicated number.

yeah, it is 63360 into 1 mile. quite absurd but what can I do :(

The circumference I get is .001289163652 mi.

Move out of the US haha

Ok so if the car is moving at 55mi/h and the circumference of the nail is ... that many miles, then how many revolutions will be made in an hour?

If only it were that simple!

Thanks for your help, I have it understood now! :)

It IS that simple No problem, have a nice day.

## 1. What is the difference between angular and linear motion?

Angular motion refers to the movement of an object around an axis, while linear motion refers to the movement of an object in a straight line.

## 2. How are angular and linear motion related?

Angular motion can be converted into linear motion through the use of gears, pulleys, or other mechanical devices. Additionally, linear motion can be broken down into its components to analyze the angular motion of an object.

## 3. How is angular motion measured?

Angular motion is measured in radians or degrees, depending on the system being used. Radians are the preferred unit of measurement as they are based on the radius of the circle and are independent of the size of the circle.

## 4. What are some real-world examples of angular and linear motion?

Angular motion can be seen in the rotation of a wheel, the spinning of a top, or the swinging of a pendulum. Linear motion can be observed in the movement of a car, the trajectory of a ball, or the sliding of a drawer.

## 5. How do angular and linear motion affect each other in everyday life?

Many everyday objects and systems involve a combination of angular and linear motion. For example, a bicycle uses both angular motion (from the rotation of the pedals) and linear motion (from the movement of the wheels) to propel the rider forward. Understanding the relationship between these two types of motion is important in fields such as engineering, physics, and robotics.

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