Rotational Dynamics class 12 solution notes [PDF] |NEB||physics|Mechanic's|

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Rotational dynamics is the study of the motion of objects that rotate around a fixed axis. It is a fundamental concept in physics that is important in many fields, including engineering, astronomy, and biology. In this article, we will explore the basic principles of rotational dynamics, including torque, angular velocity, and angular acceleration.

Torque is the force that causes an object to rotate around an axis. It is measured in units of newton-meters (Nm). The magnitude of torque depends on the force applied and the distance between the force and the axis of rotation. For example, consider a door that is hinged at one end. If you push on the door near the hinge, you will not be able to open it easily because the distance between the force and the axis of rotation is small. However, if you push on the door near the handle, you will be able to open it more easily because the distance between the force and the axis of rotation is greater.

The direction of torque depends on the direction of the applied force and the orientation of the axis of rotation. If the force is applied perpendicular to the axis of rotation, the torque will be maximum. If the force is applied parallel to the axis of rotation, the torque will be zero. If the force is applied at an angle to the axis of rotation, the torque will be intermediate.

Angular velocity is the rate at which an object rotates around an axis. It is measured in units of radians per second (rad/s). The direction of angular velocity is perpendicular to the plane of rotation and is determined by the right-hand rule. If you curl your right hand in the direction of rotation, your thumb will point in the direction of the angular velocity.

Angular acceleration is the rate at which an object's angular velocity changes. It is measured in units of radians per second squared (rad/s^2). The direction of angular acceleration is perpendicular to the plane of rotation and is determined by the right-hand rule. If you curl your right hand in the direction of angular acceleration, your thumb will point in the direction of the change in angular velocity.

The relationship between torque, angular velocity, and angular acceleration is described by the rotational analog of Newton's second law of motion. This law states that the net torque acting on an object is equal to the object's moment of inertia multiplied by its angular acceleration. The moment of inertia is a measure of an object's resistance to rotational motion and depends on the distribution of mass around the axis of rotation. For example, a thin rod will have a smaller moment of inertia than a solid sphere of the same mass because most of the mass of the rod is concentrated near its ends, which are far from the axis of rotation.

The law of conservation of angular momentum is another important principle in rotational dynamics. It states that the total angular momentum of a system is conserved if no external torque acts on the system. Angular momentum is defined as the product of an object's moment of inertia and its angular velocity. For example, when a figure skater spins, she starts with her arms outstretched and then pulls them in toward her body. This reduces her moment of inertia and increases her angular velocity, causing her to spin faster.

Applications of rotational dynamics can be found in many fields. For example, in engineering, it is important to understand the principles of rotational dynamics when designing machines that involve rotating parts, such as engines, turbines, and gears. In astronomy, rotational dynamics is used to study the motion of planets and stars, as well as the formation of galaxies. In biology, rotational dynamics is important in understanding the motion of organisms that move by rotating, such as bacteria and flagella.

In conclusion, rotational dynamics is the study of the motion of objects that rotate around a fixed axis. It involves concepts such as torque, angular

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