# Torque, radius, force a common experiment in physics

• the7joker7
In summary, the conversation discusses a common physics demonstration involving a ball at the end of a board elevated at an angle of theta. A cup is attached to the board to catch the ball when the support stick is removed. Mathematical equations, including torque and conservation of energy, are mentioned as possible approaches to understanding the experiment. The main question is how to mathematically explain why the ball lags behind the falling board when the angle is less than 35.3 degrees and how to determine the position of the cup for the ball to fall into it at that angle.
the7joker7

## Homework Statement

A common physics demonstration consists of a ball resting at the end of a board of length L that is elevated at an angle of theta with the horizontal. A light cup is attached to the board at Rc (Rc is a distance up the board from the bottom, it is not past the support stick) so that it will catch the ball when the support stick is suddenly removed. a) show that the ball will lag behind the falling board when theta < 35.3 and b) the ball will fall into the cup when the board is supported at this limiting angle and the cup is placed at
Rc = (2L)/(3cos(theta))

## Homework Equations

F*r*sin($$\theta$$) = $$\tau$$

## The Attempt at a Solution

We did this in class today actually, and I know this experiment works because of the torque involved. That is, because the stick has a radius of l, the end of it will fall faster than the ball, which doesn't have any sort of torque to speak of. The longer a stick, the faster the end moves when the other end is moved even slightly, basically. But while that's a fine English-based answer, I need something more...mathematical, and I don't really know how to approach this one mathematically.

I know that torque can be calculated using the equation F*r*sin(\theta), but I don't really know what to do with that information. I'm thinking that I need to use some sort of conservation of energy equation, but I'm not sure which one would be appropriate. Any help would be greatly appreciated!

Torque, radius, and force are all important concepts in the field of physics, and they are commonly used in experiments to demonstrate various principles. In this particular experiment, we can see how these three factors play a role in the movement of the ball and the board.

Firstly, let's define torque as the measure of a force's ability to cause rotational motion. In this experiment, the force of gravity is acting on the ball and the board, causing them to move in a circular motion around the pivot point (the end of the board). The radius, or the distance from the pivot point to the point of application of the force, is also a crucial factor in determining the torque. The longer the radius, the greater the torque will be.

Next, we have the force of gravity, which is acting on both the board and the ball. This force is what causes the objects to move in a circular motion around the pivot point. When the support stick is suddenly removed, the board and the ball experience a downward force due to gravity. However, due to the difference in their radii, the board experiences a larger torque and thus falls faster than the ball.

Now, let's consider the angle theta, which is the angle between the board and the horizontal. This angle also plays a role in determining the torque, as seen in the equation F*r*sin(theta) = tau. As the angle increases, the torque also increases, which results in a faster falling board.

To answer part a) of the problem, we can use the equation mentioned above to show that when theta is less than 35.3 degrees, the torque is not enough to overcome the inertia of the ball, causing it to lag behind the board as it falls.

For part b), we can use the equation to determine the optimal position of the cup, which is at Rc = (2L)/(3cos(theta)). This is the point where the ball will fall directly into the cup when the board is supported at the limiting angle of theta.

In conclusion, this experiment demonstrates the relationship between torque, radius, and force in a real-life scenario. By understanding these concepts, we can better understand the behavior of objects in motion and predict their movement in various situations.

## 1. What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied.

## 2. Why is radius important in experiments involving torque?

Radius is important in torque experiments because it determines the distance from the center of rotation to the point where the force is applied. This distance affects the amount of torque produced and can be used to manipulate the amount of force applied to an object.

## 3. How does force affect torque?

Force directly affects torque. The greater the force applied to an object, the greater the torque produced. This relationship is described by the equation: torque = force x distance.

## 4. What is the purpose of conducting experiments involving torque, radius, and force?

The purpose of these experiments is to study the principles of rotational motion and understand how torque, radius, and force are related. These experiments can also help us understand how to manipulate and control rotational motion in real-world applications.

## 5. What are some real-world applications of torque experiments?

Torque experiments are used in various fields such as engineering, physics, and sports. Some examples of real-world applications include designing and building machines such as engines and turbines, understanding the mechanics of sports equipment like golf clubs and baseball bats, and studying the movement of objects in space.

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