Dynamics Rotational Motion

Rigid bodies have the ability to move in both translation and rotation. As a result, both the linear and angular velocities must be assessed in such situations. To make these issues more understandable, the translational and rotational motions of the body must be defined separately. In this article, the dynamics of an item rotating around a fixed axis will be explained.

Rigid body

The definition of a rigid body is a system of particles in which the distance between each pair of particles is constant. A rigid body is one whose shape is precisely defined and unchangeable.

Rotational motion

Rotational motion is defined as the movement of a body in a circular path around a fixed point in space.

The motion of a body that does not deform or change shape, in which all of its particles revolve around an axis at the same angular velocity. For example, the rotation of the earth on its axis, the rotation of a vehicle’s wheel, gears, motors, and so on.

Physical quantities related to rotational motion

Consider a solid body that rotates around an axis and moves its particles in circular patterns. Let r represent the radius of a particle’s path. Let v be the particle’s linear velocity.

1. Angular displacement (): The angle formed by a straight line connecting a particle and the circular path’s centre.
2. Angular velocity (): The angular velocity of a particle is the rate at which its angular displacement changes.
3. If is the angular displacement of a particle during t seconds, then its angular velocity is equal to ω=θt.
4. The SI unit of angular velocity is rad s-1.
5. It is a vector quantity.
6. Angular acceleration: The angular acceleration of a particle is the rate at which its angular velocity changes.

Rotational motion about a fixed axis

Because the axis is fixed, only torque components in the same direction as the fixed axis are considered. Only these components have the power to rotate the body around its axis. Perpendicular to the rotation axis, a component of the torque will tend to turn the axis away from its current position. The influence of the perpendicular components of the (external) torques is supposed to be cancelled allowing the axis to remain in its fixed location. As a result, the torques’ perpendicular components do not need to be taken into account. This indicates that for calculating torques on a rigid body, this is the formula to use.

• Only forces in planes perpendicular to the axis must be taken into account. Forces parallel to the axis produce torques that are perpendicular to the axis and don’t need to be taken into account.
• Only the perpendicular to the axis components of the position vectors must be evaluated. Torques perpendicular to the axis will result from position vector components along the axis and do not need to be considered.

Moment of inertia

A measurement of an object’s resistance to rotational change is called the moment of inertia. I represent the moment of inertia, which is measured in kilograms per square metre (kg m2) It’s written as: I=Mr²

where m denotes the mass of the particle and r denotes the distance from the rotation axis.

Torque

The turning action of force about the axis of rotation (the point at which an object rotates) causes an object to rotate around an axis. Torque accelerates an item in an angular direction in the same manner that force accelerates an object in a linear direction. It’s also known as the moment of force. The symbol is used to represent it. For example, people use torque to close the door. We apply torque to tighten the nut.

Rotational kinetic energy

The energy of motion of a rotating object is known as rotational kinetic energy. In rotational motion, rotational kinetic energy serves the same purpose as translational kinetic energy does in translational motion. The linear kinetic energy of a body is determined by its mass and speed; similarly, the rotational kinetic energy is determined by the moment of inertia (rotational mass) and angular velocity.

The formula for calculating the rotational kinetic energy is: E=Iω². Here, I is the moment of inertia and is the angular velocity.

Angular momentum

Any body that rotates around a point or axis can be described as having angular momentum. The angular momentum in rotational motion is identical to linear momentum in linear motion, just as the moment of force (Torque) in rotational motion is analogous to force in linear motion. L=mvr is how the angular momentum formula is written. Here, m is the mass, v is the linear velocity and r is the radius.

Conclusion

The dynamics of rotating motion are quite similar to those of linear or translational motion. The effects of force and mass on motion are the subject of dynamics. We shall identify direct analogues to force and mass for rotational motion that behave just as we would expect from our previous experiences.