![]() ![]() ![]() Where w(t) is the angular velocity and C 1 is a constant. Integrate the above equation with respect to time, to obtain angular velocity. Where α is the angular acceleration, which we define as constant. The derivations that follow are of the exact same form as the equations derived for rectilinear motion, with constant acceleration. The easiest way to derive these equations is by using Calculus. With angular acceleration as constant we can derive equations for the angular position, angular displacement, and angular velocity of a rigid body experiencing rotation about a fixed axis. These are important quantities to consider when evaluating the rotational kinematics of a problem.Ī common assumption, which applies to numerous problems involving rotation about a fixed axis, is that angular acceleration is constant. Given the angular position of the rigid body we can calculate the angular displacement, angular velocity, and angular acceleration. ![]() This angle can be measured in any unit one desires, such as radians, or degrees.Įvery point in the rigid body rotates by the same angle θ(t). ![]() In the figure, the angle θ(t) is defined as the angular position of the body, as a function of time t. This type of motion occurs in a plane perpendicular to the axis of rotation. The figure below illustrates rotational motion of a rigid body about a fixed axis at point O. It is very common to analyze problems that involve this type of rotation – for example, a wheel. Rotation about a fixed axis is a special case of rotational motion. According to the law of conservation of angular momentum, if there is no external force acting, the total angular momentum of a rigid body or a system of particles is conserved.Rotational Motion Rotation About A Fixed Axis The angular momentum about an axis of rotation is a vector quantity, whose magnitude is equal to the product of the magnitude of momentum and the perpendicular distance of the line of momentum from the axis of rotation and the direction is perpendicular to the plane containing the momentum. The next important topic in our notes on the system of particles and rotational motion is Angular Momentum. Must Read: Experiment With Diverse Career in Physics Angular Momentum and Law of Conservation Angular Momentum The given theorems are- The Theorem of Perpendicular AxisĪs per this theorem, the moment of inertia I of the body for a given perpendicular axis is always equal to the sum of moments of inertia of the body about two axes always at an angle of 90° to each other in the plane of that body and meeting at a point where the perpendicular axis passes,Īccording to the theorem of the Parallel axis, the moment of inertia I of a body about any given axis is always equal to its moment of inertia about a given parallel axis through the concept of centre of massIcm. Credit: Internet Theorems of System of Particles and Rotational MotionĬhapter 7 of Physics Class 11 System of Particles and Rotational Motion consists of two important theorems which are necessary to understand in order to have a strong grip on this topic. About a given axis, the moment of inertia of a rigid body can be calculated as the sum of the products of the masses of the particles composing the body and the square of their respective perpendicular distance of particles from the axis. The Moment of inertia of a Rigid body is defined as the rotational inertia of that body. ![]()
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