Rotation of Rigid Bodies

Introduction

A rigid body is a simplified version of a solid body that does not deform. In other words, regardless of external forces acting on a rigid body, the distance between any two points remains constant over time.

An example of a rigid body is a metal rod.

When a rigid body is in pure rotational motion, all of its particles rotate at the same angle and for the same amount of time. As a result, all particles have the same angular velocity and acceleration.

When a stiff item spins, every part of it (every atom) travels in a circle, covering the same angle in the same period of time. We can’t measure the top’s rotation speed by giving a single velocity because all of the velocities are different. We may, however, consistently quantify its rotational speed in terms of angle per unit time. Let the angle, measured in a circle around the axis, denote the position of some reference point on the top. We use radians to measure all angles for reasons that will become clearer later. Then every change in the angular position of any point on the top can be expressed as d, and during a given time interval dt, all regions of the top have the same value of d. The angular velocity is defined as ω (Greek omega), which is similar to, but not the same as, the quantity ω we defined earlier to describe vibrations. The relationship between ω and t is exactly analogous to that between x and t for the motion of a particle through space.

Every part of a rigid object (every atom) moves in a circle, covering the same angle in the same amount of time when it rotates. Each atom has a unique velocity vector. We can’t measure the top’s rotation speed by giving a single velocity because all of the velocities are different. We may, however, consistently quantify its rotational speed in terms of angle per unit time. Let the angle, measured in a circle around the axis, denote the position of some reference point on the top. We use radians to measure all angles for reasons that will become clearer later. Then every change in the angular position of any point on the top can be expressed as dθ, and during a given time interval dt, all regions of the top have the same value of dθ. The angular velocity is defined as  ω (Greek letter omega).

                       ω = dθ/dt

Rotational Motion Examples:

Rotatory motion is defined as the rotation or spinning of an item around its axis. The motion of a spinning top, the rotation of the earth and other planets, the movement of clock hands, and so on are all examples of rotatory motion.

1. Rotation of earth: The motion of the earth and other planets around their respective axes is an example of rotatory motion, as the name implies. Inertia causes the heavenly bodies to revolve around their central position.
2. Wheels of a moving vehicle: A vehicle’s wheels rotate in relation to the axle. The spinning of the wheels assists in moving the vehicle forward or backwards. The rotatory motion of the wheels is demonstrated, whereas the car’s motion is the result of the conversion of rotational motion into linear motion.
3. Fan blades: A fan’s blades are connected to a central hub, which is connected to a motor located within the appliance’s internal circuitry. The motor is triggered when an electric current is given to the fan’s electrical circuit. The motor then converts electrical energy to mechanical energy, causing the fan blades to spin and move in a rotatory motion.
4. Spinning Top: A spinning top is a toy with a sharp tip that is wound in a thread on the outside. One of the best illustrations of rotatory motion is the movement of a spinning top. When the spinning top is placed on a surface with only its pointed end in contact with the ground and the thread is tugged firmly, the top spins around its own axis until all of the top’s energy is gone.
5. Ferris Wheel: A Ferris Wheel is a popular attraction at any carnival or funfair. It is a large metallic wheel that serves as an amusement ride. The Ferris Wheel’s rim is made up of a number of cabins that transport passengers. The wheel rotates around its centres point when the motor attached to the ride is powered up. As a result, the movement of a Ferris Wheel in real life clearly exhibits rotatory motion.

Rotational motion:

“The motion of an object around a circular route in a set orbit is known as rotational motion.” This is how we define rotational motion.

Rotating motion has characteristics that are quite similar to linear or translational motion. The linear motion equations are connected to many of the equations for rotating object mechanics. In rotational motion, only rigid bodies are taken into account. A rigid body is an entity that has a mass and a rigid shape.

Conclusion:

Forces that are parallel to the axis produce torques that are perpendicular to the axis and do not need to be considered. Also, only the perpendicular to the axis components of the position vector are taken into account. Components of position vectors along the axis produce torques perpendicular to the axis. Hence, they should be ignored.

The total work done by all the forces acting on an object is equal to the change in the object’s kinetic energy, according to the work-energy principle.

The torque is the basis for the work-energy principle in rotational motion. When a force is applied, the object is said to be in a balanced state if its displacements and rotations are equivalent to zero work.