Dynamic

Physics is all about dynamism, it talks about the dynamics of circular motion, in which we consider the example of rotational motion, which we can understand mathematically with the help of rotational dynamics equations and applying the formula of rotational motion in rotational motion dynamics.

We also learn about static and dynamic equilibrium physics. In static and dynamic equilibrium Physics, we understand that when all the forces remain balanced on the body at rest is the static equilibrium and if it is moving with all the balanced forces, it is a dynamic equilibrium.

On this page, we will learn about all these in detail.

Static and Dynamic Equilibrium Physics

When all the forces acting on the body are balanced, provided that the body is static in relation to the frame of reference, then a body possesses a static equilibrium.

However, when all the forces on the body remain balanced even if the body is moving, we can say that the body possesses a dynamic equilibrium.

Now, let’s understand the static and dynamic equilibrium Physics one-by-one:

Static Equilibrium Physics

In other words, the static equilibrium is the state of equilibrium in which the net external force and torque acting on the body is zero.

For example, a woman snoring on a static merry-go is said to possess a static equilibrium.

A few more examples of static equilibrium are:

1. A man working in front of the laptop stays in a balanced position because all the external forces acting on him remain balanced.

2. Consider a mug kept on the corner of the dining table. Here, the gravitational force of attraction tries to pull it down; however, the counter-balanced force offered by the table balances it and saves it from falling.

So, in the above three examples, we notice that no object moves in any direction, and remains static until something changes.

Now, let’s suppose that your dog bumps the table, offsetting the balance of the mug. It topples over the table and eventually falls. This happened because the balancing force of the table countering the gravitational act shakes and it loses its own balance, thereby making the mug fall.

Dynamic Equilibrium Definition Physics 

In other terms, dynamic equilibrium Physics is the state of equilibrium in which the net external force and the torque acting on the body moving with a constant velocity is zero.

For example, Imagine a jet flying through the sky when there is absolutely no air movement, i.e., a condition highly unlikely ever to exist. 

In this example, the jet has the following four fundamental forces acting upon it: 

1) Gravity trying to pull the jet down, 

2) A dynamic lift generated by the jet's wings, trying to pull it up, 

3) thrust (propulsive force) from the jet's engines, trying to propel the jet forward, and 

4) air resistance, trying to push the jet backward until it stops its forward motion. 

We notice that as long as the jet flies at the perfect level, there are no changes in the air around it, and engines produce a constant thrust, the force of gravity under it does not change, here, the jet settles into a "dynamic equilibrium" where its upward or downward motion remains constant, and its forward motion also remains invariant. 

Though it is moving, its rate and direction of movement remain constant.

Dynamics of Circular Motion

In a circular motion, a particle makes a move around the circumference of a circle. The motion of the body can be uniform, with the constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.

The dynamics of circular motion are:

Let’s consider an object undergoing a circular motion on a circular path of the radius (r) with angular velocity (ω), having tangential velocity (v) and radial acceleration (ac), then,

1) The net external force acting on the particle must be directed towards the center which is known as centripetal force.

2) The cross product of angular velocity and the tangential acceleration is zero because the angle between them is zero.

3) The angular acceleration and angular velocity of the body remain in the same direction.

The angular velocity ()is the amount of rotation made by the particle in unit time. It is a vector quantity that possesses two directions, viz: clockwise and anti-clockwise.

In the case of uniform circular motion, the speed of the object remains constant, while the object has an acceleration towards the center is its circular path which is given as;

ac = v2/r

Let the mass of the particle be ‘m’, then by Newton’s second law of motion, we have:

F = m * ac

F = mv2/r

Rotational Dynamics Equations

Let us consider an example of rotational motion:

A biker in a rider mania is making rounds in a spherical shell in rotational motion. Here, a string is tied on his back with the support of the rod along the axis of the shell. So, the formula of rotational motion in this case is:

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Where,

I = a moment of inertia

R = radius of gyration

M = mass of the biker

Second Example,

In our mythology, we don’t make the entire round around the Lord Shivling. We cross half-path and return to our fixed point and make another half-round. Here, the motion seems like a motion of the ring along the axis. 

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The formula of rotational motion, in this case, is as;