# Rotational Mechanics (Pulley and Mass)

• Californiarol
In summary, the problem involves a 10 kg mass hanging from a rope attached to a uniform wheel on a frictionless axle. The mass accelerates at 4.9m/s^2 and the forces acting on the system are weight and tension. The tension can be calculated using T - W = ma, and the mass of the wheel can be calculated using the equation \tau = I \alpha, where tau is torque, I is moment of inertia, and alpha is angular acceleration.
Californiarol

## Homework Statement

I am studying for a final exam and I do not know how to solve this problem:

A 10 kg mass hangs by a rope of negligible mass. The upper end of the rope is attached to and is wound around the other edge of a solid uniform wheel which is free to rotate on a horizontal frictionless axle. (So its basically a pulley (a wheel with a single mass hanging down one side)). The 10kg mass is released from rest and accelerates 4.9m/s^2

a) What are all the forces acting on this system?

b) What is the tension of the rope as the 10kg mass falls?

c) Calculate the mass of the wheel.

2. The attempt at a solution

a) For this part, I put the obvious ones, ie: weight, and tension. Are there any others, especially with regard to the wheel?

b) For the y-component, we have T-W = -4.9m/s^2 and solving for T gives 49N. However, this seems kind of trivial and the question is worth 5 points so I'm not certain this is right.

c) I have no idea about this part. I know angular acceleration = 4.9/R and that's about as far as I got on this part.

Any help would be appreciated!

Californiarol said:

## Homework Statement

I am studying for a final exam and I do not know how to solve this problem:

A 10 kg mass hangs by a rope of negligible mass. The upper end of the rope is attached to and is wound around the other edge of a solid uniform wheel which is free to rotate on a horizontal frictionless axle. (So its basically a pulley (a wheel with a single mass hanging down one side)). The 10kg mass is released from rest and accelerates 4.9m/s^2

a) What are all the forces acting on this system?

b) What is the tension of the rope as the 10kg mass falls?

c) Calculate the mass of the wheel.

2. The attempt at a solution

a) For this part, I put the obvious ones, ie: weight, and tension. Are there any others, especially with regard to the wheel?

b) For the y-component, we have T-W = -4.9m/s^2 and solving for T gives 49N. However, this seems kind of trivial and the question is worth 5 points so I'm not certain this is right.

c) I have no idea about this part. I know angular acceleration = 4.9/R and that's about as far as I got on this part.

Any help would be appreciated!

For part (b), shouldn't you be writing T - W = ma, which is T - W = m(4.9) ? Just a small thing, but small things lead to errors.

Now about part (c), recall that $$\tau = I \alpha$$
where tau is the torque, I is the moment of inertia, and alpha is the angular acceleration. That will allow you to calculate the mass of the wheel.

## 1. What is rotational mechanics?

Rotational mechanics is a branch of physics that deals with the motion of objects that rotate around an axis. It involves the study of forces, torque, and angular momentum in relation to rotational motion.

## 2. What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove and a rope or cable that runs along the groove. It is used to change the direction of a force and to lift or move objects by using the principle of mechanical advantage.

## 3. How does mass affect rotational mechanics?

Mass is an important factor in rotational mechanics as it affects the amount of torque needed to rotate an object, as well as the object's moment of inertia. The greater the mass, the greater the force needed to rotate the object and the slower the rotation.

## 4. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a stationary object and only changes the direction of the force, while a movable pulley is attached to the object being lifted and reduces the amount of force needed to lift it.

## 5. How do I calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system can be calculated by dividing the output force (the weight being lifted) by the input force (the force applied to the rope or cable). The more pulleys in the system, the greater the mechanical advantage.

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