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The basics of rotational motion you need to know


The basics of rotational motion you need to know

Rotational motion is experienced by rigid bodies as well as translational motion. Therefore, the linear and angular velocities need to be analyzed in such cases. This problem can be simplified by separating the translational and rotational motion of the body. This article will talk about how an object rotates around a fixed axis.

What is Rotational Motion?

An object's rotation can be defined as its motion around a circle in a fixed orbit.

Rotational Motion is entirely analogous to translational or linear motion. Several of the equations for the mechanics of rotating objects are also applicable to linear motion. However, only rigid bodies are considered in rotational motion. An object with a fixed mass and shape is considered rigid.

Rotation around a fixed axis

Whenever a rigid body undergoes a rotation around a fixed axis, we only need to consider forces acting in planes perpendicular to that axis.

Examples of rotational motion:

  • Example of Rotation around a Fixed Point The rotation of the ceiling fan blades, rotation of the minute hand and hour hand in the clock, as well as opening and closing the door, are a few examples of rotation about a fixed point.

  • Example of rotation around an axis
    The motion of a rotating axis includes both translational and rotational motion. For example, pushing a ball from an inclined plane is an excellent example of rotation about an axis of rotation. During translation, the ball reaches the bottom of the inclined plane, and the ball's motion occurs when it rotates about its axis, which is rotational motion.
    Earth's motion is also an example of rotation about an axis of rotation. In addition to rotating around its axis every day, the earth also revolves around the sun once a year. Translation and rotation are displayed in this classic example of motion.

Dynamics of rotational motion

  • Moment of Inertia
    As the rotation of an object changes, the moment of inertia also changes. The symbol symbolizes the moment of inertia I, measured in kilogram metre2 (kg m2). According to the following equations, the moment of inertia is:
    I = Mr2, where m is the particle's mass and r is the particle's distance from the axis of rotation. A particle's moment of inertia is determined by its mass; the larger the mass, the greater the moment of inertia.

  • Torque
    Torque can be defined as the twisting effect of a force applied to a rotating object r degrees away from its axis of rotation. On a mathematical level, this relationship looks like this:
    τ = rxF

  • Angular Momentum
    An object's angular momentum L measures the difficulty of bringing it to rest after rotating. It can be calculated as follows:
    L = ∑ rxp

Rotational Motion and Work-Energy Principle

Work-energy theory states that the total work done by all forces acting on a system will equal the change in kinetic energy. In the concept of work energy, torque is used to describe rotational motion. When a force is applied, an object is balanced if its displacements and rotations account for zero work.

The object rotates in a small amount when it is a rigid body. Then the linear displacement is calculated as Δr = rΔθ. It is perpendicular to r.

As a result, the work done is

ΔW = F perpendicular to Δr

ΔW = F Δr sin φ

ΔW = Fr Δθ sin φ

ΔW = τΔθ

Increasing the number of forces acting will increase the work done

ΔW = (τ1 + τ2 + ......) Δθ

However, we know that all forces are the same. Therefore, there will be no work done, which is

τ1 + τ2 + ...... = θ

Thus, rotational motion can be explained by the work-energy principle.

Relations among torque, a moment of inertia, and angle of acceleration

Those who have ever pushed a merry-go-round can understand the rotational dynamics; the angular velocity changes when a force is applied to a merry-go-round. Likewise, bicycle wheels also spin when force is used as the force increases, the angular acceleration produced in the wheel increases. As a result, we can say that there is a relationship between forces, masses, angular velocity, and angular acceleration.

Take a look at the wheel of the bike. A wheel's acceleration, for example, is the result of angular forces F acting on it. R is the radius of the wheel. We know the force acts perpendicularly to the radius. In addition, we know that,

F = ma

Where a is acceleration = rα


F = mrα

As we have learned, torque is the effect of force turning. Thus,

τ = Fr

rF = mr2α

τ= mr2α

We may therefore say that the last equation is the rotational analog of F = ma, such that torque is equivalent to force, angular acceleration is equivalent to acceleration, and rotational inertia is equal to mass. As well as rotational inertia, a moment of inertia is also commonly used.

Angular acceleration and torque are related by the moment of inertia

net τ = Iα

α = net τ/I

Where net τ is the total torque.


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