Angular Mechanics

Angular mechanics is a branch of mechanics. Angular mechanics involves the study of motion of a body in a rotational or a circular way. The angular momentum and torque are the most important and responsible part for angular mechanics. When the force is applied to a body that causes it to rotate then it creates torque. Similar to force, torque also acts to angularly accelerate a spinning object. The equation for torque (expressed as Γ here) looks very much like force in a linear motion (F = ma) because the torque is analogous to the force in rotational motion.

Γ = Iα

Instead of mass, we have rotational inertia(mass and inertia are analogous to each other). Instead of linear acceleration, we have angular acceleration(linear acceleration and angular acceleration are analogous to each other).

Now, if a force is applied linearly to make an object move, its torque is defined as:

Γ  = F × r

In angular mechanics, angular momentum, moment of momentum, or rotational momentum is a quantity in a rotational motion is analogous to linear momentum in translation motion. Just as linear momentum is equal o the product of mass and linear velocity, angular momentum is equal to the product of M.I. and angular velocity. It is also a vector quantity.

L = r × p = r × mv,

L =Iw

Where,

r- radius of vector,

P-linear momentum,

m- mass of the body,

v- velocity of a body,

I-moment of inertia,

w-angular velocity

Where there is no net external torque, angular momentum is conserved in a system and its conservation helps explain many diverse phenomena. Let us see one example- the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The another example is-a very high rotational rates neutron stars. It means, angular momentum conservation has numerous applications in physics and engineering.