# How does torque relate to changes in angular momentum?

• fro
In summary, The conversation discusses finding the magnitude of torque acting on an object when its angular momentum changes by 20kg*m^2/s in 4 seconds. The formula L=Iw and T=I*angular acceleration are suggested, but the individual is unsure how to use them. They also make a useful observation that for a constant acceleration, alpha=delta omega/delta t. The formula tau=delta L/delta omega times alpha is used to find the torque, and the individual is guided to use delta omega=alpha times delta t. The final formula for torque is derived to be tau=delta I/delta t, which is recommended to remember.
fro
I have no clue as to how to solve this. Any hints/suggestions will be helpful.

Problem: An object's angular momentum changes by 20kg*m^2/s in 4 seconds. What magnitude of torque acted on the object?

Do you know of any expressions which relate a change in momentum to a torque? Or perhaps a torque to an angular acceleration?

Hootenanny said:
Do you know of any expressions which relate a change in momentum to a torque? Or perhaps a torque to an angular acceleration?

Maybe I could use L = I*w and T = I*angular acceleration? But I don't know what to do after that.

It may be useful to note that for a constant acceleration;

$$\alpha = \frac{\Delta\omega}{\Delta t}$$

Hootenanny said:
It may be useful to note that for a constant acceleration;

$$\alpha = \frac{\Delta\omega}{\Delta t}$$

By your equation, angular acceleration should be 5kg*m^2. Not sure how and where to plug it into get the answer.

fro said:

By your equation, angular acceleration should be 5kg*m^2. Not sure how and where to plug it into get the answer.
Another useful observation; from your equation (I is constant);

$$\Delta L = I \Delta\omega \Leftrightarrow I = \frac{\Delta L}{\Delta \omega}$$

Hootenanny said:
Another useful observation; from your equation (I is constant);

$$\Delta L = I \Delta\omega \Leftrightarrow I = \frac{\Delta L}{\Delta \omega}$$

$$\Delta L = 20{kg} \cdot{m^2}$$
$$\alpha = \frac{20kg\cdotm^2}{4s} = {5kg} \cdot {m^2}$$
$$\tau = \frac{\Delta L}{\Delta \omega} \times \alpha$$
$$\tau = \frac{20kg\cdot m^2}{\Delta \omega} \times {5kg} \cdot {m^2}$$

So, how would I find $$\Delta \omega$$?

Last edited:
From my previous posts;

Hootenanny said:
$$\alpha = \frac{\Delta\omega}{\Delta t}\;\;\;\;\;\; (1)$$

Hootenanny said:
$$\Delta L = I \Delta\omega \Leftrightarrow I = \frac{\Delta L}{\Delta \omega}\;\;\;\;\;\; (2)$$

Using those to facts and the formula;

$$\tau = I\alpha \stackrel{(1)\;\&\;(2)}{\Rightarrow} \tau = \frac{\Delta L}{\Delta \not{\omega}} \cdot \frac{\Delta\not{\omega}}{\Delta t}$$

$$\therefore \boxed{\tau = \frac{\Delta I}{\Delta t}}$$

This is a good formula to remember

## 1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is a vector quantity that takes into account the object's mass, speed, and distance from the axis of rotation.

## 2. How is angular momentum calculated?

The formula for calculating angular momentum is L = Iω, where L is angular momentum, I is the moment of inertia, and ω is the angular velocity.

## 3. What causes a change in angular momentum?

A change in angular momentum can be caused by a torque, or a force that causes rotation. This torque can be applied externally or can result from the redistribution of mass within the rotating object.

## 4. How does angular momentum change in a closed system?

In a closed system, the total angular momentum remains constant. This is known as the law of conservation of angular momentum. If one part of the system experiences a change in angular momentum, another part of the system must experience an equal and opposite change in order to maintain the total angular momentum.

## 5. What are some real-world examples of changes in angular momentum?

One example of a change in angular momentum is when a figure skater pulls in their arms while spinning, causing them to rotate faster due to a decrease in their moment of inertia. Another example is when a gyroscope's axis is tilted, causing it to precess or rotate in a different direction.

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