# Falling mass attached to wheel

• axe34
In summary, the conversation discusses the use of energy and torque methods to solve for the angular momentum of a system including a falling mass and a rotating cylinder attached by a non-stretching cable. The correct torque is determined to be (mg-T)R, and the tension in the cable is found to be internal and not affecting the angular momentum of the system.
axe34

## Homework Equations

I am aware that this can be done via energy methods. However, I wish to do it via:

integral between t1 and t2 of Torques about point (say centre of the wheel) = change in angular momentum of the wheel.

## The Attempt at a Solution

The torque is mgR. t1 is zero.
I get that the block hits the floor at t = (square root of 2gh)/g

When I use the change in angular momentum equation, I get w (omega) final as (2.m. (square root of 2gh))/MR but this supposedly is not correct.

Any ideas??

axe34 said:
I get that the block hits the floor at t = (square root of 2gh)/g

This cannot be correct. It is only correct when the cylinder is massless. Consider the case where the cylinder is much more massive than the attached mass - the acceleration will be much lower due to the torque needed to accelerate the rotation of the cylinder. Your result must depend on the ratio of masses. It seems to me that you are ignoring how the cylinder and hanging mass are affecting each other through the tension in the string.

I've looked into this a bit further - I was neglecting the possible tension in the cable. I thought that a non-stretching cable meant no tension but apparently not!

You do not need to compute the tension. If you consider the system including both cylinder and falling mass, the tension is internal and does not affect the angular momentum.

Yes, but the torque is not just mgR now, but probably (mg-T)R

axe34 said:
I've looked into this a bit further - I was neglecting the possible tension in the cable. I thought that a non-stretching cable meant no tension but apparently not!
Non-stretching cable means that its length does not change.
There is tension in the cable. That tension acts both on the cylinder and the falling mass.

axe34 said:
Yes, but the torque is not just mgR now, but probably (mg-T)R

This is because you are now considering the cylinder only as your system. If you consider the cylinder and hanging mass as one system as I suggested, then:
Orodruin said:
If you consider the system including both cylinder and falling mass, the tension is internal and does not affect the angular momentum.
The torque on the full system (including both cylinder and hanging mass) is definitely still mgR. What you have to figure out is what the angular momentum is.

## What is the purpose of studying a falling mass attached to a wheel?

The purpose of studying a falling mass attached to a wheel is to understand the relationship between the weight of the mass, the radius of the wheel, and the speed at which the mass falls. This can help in designing efficient mechanisms for lifting and lowering objects, such as elevators or cranes.

## How does the weight of the falling mass affect the speed of the wheel?

The weight of the falling mass affects the speed of the wheel by increasing the torque, or rotational force, on the wheel. This causes the wheel to rotate faster, which in turn increases the speed of the falling mass.

## What is the significance of the radius of the wheel in this scenario?

The radius of the wheel is significant because it determines the amount of leverage the weight of the falling mass has on the wheel. A larger radius will result in a greater torque and therefore, a faster rotation of the wheel.

## How does the angle of the wheel affect the speed of the falling mass?

The angle of the wheel, or the angle at which the mass is attached to the wheel, does not directly affect the speed of the falling mass. However, it can affect the direction of the force applied to the wheel, which can impact the speed and direction of the rotation.

## What other factors besides weight and radius can impact the speed of the wheel and falling mass?

Other factors that can impact the speed of the wheel and falling mass include friction, air resistance, and the material and shape of the wheel. These factors can either increase or decrease the efficiency of the mechanism and should be taken into consideration in the design process.

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