Tru Physics

Torque

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Tru Physics
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Introduction

Torque, also known as moment or moment of force, is a measure of the force that can cause an object to rotate around an axis. Torque is a vector quantity, meaning it has both magnitude and direction.

Definition and Formula

The torque \vec{\tau} due to a force \vec{F} acting at a point with position vector \vec{r} relative to the axis of rotation is given by:

\vec{\tau} = \vec{r} \times \vec{F}

The magnitude of the torque is given by:

|\vec{\tau}| = rF\sin\theta

where:

  • r is the distance from the axis of rotation to the point where the force is applied,
  • F is the magnitude of the force,
  • \theta is the angle between \vec{r} and \vec{F}.

Torque and Rotational Motion

Torque is the rotational analogue of force in linear motion. In the same way that force is necessary to change an object’s linear momentum, torque is necessary to change an object’s angular momentum.

The net torque on an object is equal to the rate of change of its angular momentum L:

\vec{\tau}_{\text{net}} = \dfrac{d\vec{L}}{dt}

Torque and Rotational Inertia

The effect of a torque on an object also depends on the object’s moment of inertia I, which is a measure of its resistance to changes in rotational motion. The relationship between torque, moment of inertia, and angular acceleration \alpha is given by Newton’s second law for rotation:

\vec{\tau}_{\text{net}} = I\vec{\alpha}

Static Equilibrium

In static equilibrium, an object is at rest and remains at rest. This requires both the net force and the net torque on the object to be zero. In terms of torque, this condition can be written as:

\sum \vec{\tau} = \vec{0}

Conclusion

Torque is a fundamental concept in the study of rotational motion. It has applications in many areas of physics and engineering, including mechanical engineering, structural engineering, and biomechanics. Understanding torque is crucial for designing and analyzing systems that involve rotation.

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