Understanding Torque from Angular Momentum Change

Torque is a fundamental concept in physics, closely related to the change in angular momentum. This article explores how to calculate torque when there is a change in angular momentum over a specific period. We will use a specific example to illustrate this process.

What is Torque?

Torque, often denoted by τ, is defined as the rate of change of angular momentum. Mathematically, it can be expressed as:

τ ΔL / Δt

Where:

ΔL is the change in angular momentum. Δt is the change in time.

Conceptual Differences Between Torque and Work

It is essential to distinguish between torque and work. While both involve units of newtons times meters (N?m), they represent different physical quantities. Work is the force that causes a displacement, while torque is the force that causes rotation.

Note that joules (J) are the units of work, not torque. While work involves a dot product (force times displacement), torque involves a cross product (force times distance in the direction perpendicular to the force). Therefore, it is incorrect to convert torque from N?m to joules (J).

Example Calculation

Let's apply the formula to a specific example to calculate the torque when the angular momentum changes from 1 Js to 4 Js over a period of 4 seconds.

Given Data

Inital angular momentum, Li: 1 Js Final angular momentum, Lf: 4 Js Change in time, Δt: 4 seconds

Step-by-Step Calculation

Calculate the change in angular momentum (ΔL): ΔL Lf - Li ΔL 4 Js - 1 Js 3 Js Calculate the torque (τ): τ ΔL / Δt τ 3 Js / 4 s 0.75 N?m

Conclusion

Based on the given example, the torque is 0.75 N?m.

Additional Insights

Understanding the difference between torque and work is crucial in many fields, including mechanics, engineering, and physics. Torque is a key factor in determining the rotational force in systems such as engines, motors, and rotational machinery.

It is also important to use the correct units when dealing with these concepts. Torque is always expressed in N?m, not joules (J).