# How Far Does a Coin Roll Before Stopping Given Its Angular Deceleration?

• physics1234
In summary, in this problem you need to find the distance a coin rolls before coming to rest. The coin has a diameter of 2.20 cm and starts with an initial angular speed of 15.9 rad/s. It then experiences an angular acceleration of magnitude 1.76 rad/s2, causing it to slow down. To find the distance, you can use the definition of acceleration and the angular equations. You do not need to find the time, but you could if needed.
physics1234
A coin with a diameter of 2.20 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 15.9 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.76 rad/s2, how far does the coin roll before coming to rest?

Ok, I figured out that the radius is 0.011m and then got stuck. How can you find distance without time?

You don't need to find the time, but you could find it using the definition of acceleration.

What would be the best way to do it then?

Tell me the definition of acceleration.

acceleration

The changing of an object's velocity with time.

physics1234 said:
The changing of an object's velocity with time.
In this problem you are given an initial angular velocity and angular acceleration. You know the final angular velocity is zero. You can find the angular diplacement and use that to find the distance the coin rolls. The angular equations are directly analogous to the linear equations.

physics1234 said:
The changing of an object's velocity with time.
Right, acceleration is the rate of change of velocity; analogously, angular acceleration is the rate of change of angular velocity. Now express that mathematically:
$$\alpha = \Delta \omega / \Delta t$$

You can use that to find the time. (You can also make use of any other kinematic relationships you know.)

## What is angular speed?

Angular speed is the rate at which an object rotates or moves around a fixed point. It is measured in radians per second (rad/s) or degrees per second (deg/s).

## How is angular speed different from linear speed?

Angular speed is the rate of change of angular displacement, while linear speed is the rate of change of linear displacement. In simpler terms, angular speed measures how fast an object is rotating, while linear speed measures how fast an object is moving in a straight line.

## What is the formula for angular acceleration?

The formula for angular acceleration is a = (ω2 - ω1) / (t2 - t1), where ω2 and ω1 are the final and initial angular velocities respectively, and t2 and t1 are the final and initial times.

## How does angular acceleration affect the motion of an object?

Angular acceleration determines the rate at which an object's angular velocity changes. If the angular acceleration is positive, the object's angular velocity increases, causing it to rotate faster. On the other hand, if the angular acceleration is negative, the object's angular velocity decreases, causing it to rotate slower.

## What is the relationship between angular speed and angular velocity?

Angular speed and angular velocity are closely related, but they are not the same. Angular speed is the magnitude of angular velocity, while angular velocity also includes the direction of rotation. In other words, angular velocity is a vector quantity, while angular speed is a scalar quantity.

Replies
4
Views
2K
Replies
2
Views
8K
Replies
2
Views
1K
Replies
39
Views
2K
Replies
7
Views
2K
Replies
2
Views
2K
Replies
4
Views
3K
Replies
2
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K