Angular momentum is conserved in systems where the total applied torque is 0. It is a vector property defined by magnitude and direction. Moment of inertia measures an object’s resistance to changes in rotation and is a function of mass and shape. Angular velocity is measured in radians per second and is calculated by dividing the perpendicular velocity vector by the radius. Angular momentum is found by multiplying moment of inertia by angular velocity.
The conservation of angular momentum is a fundamental concept in physics, along with the conservation of energy and the conservation of linear momentum. It states that the total angular momentum of a system must remain the same, meaning it is conserved. Angular momentum is a vector property, meaning it is defined by both a magnitude and a direction, so the conservation of angular momentum also involves vectors.
Angular momentum conservation applies to systems where the total applied torque is 0. Torque is a rotational force, such as torsion. To determine whether conservation of angular momentum applies, the sum of angular moments in the system before and after a change is added. If the angular momentum after the change minus that before the change equals 0, the angular momentum has been conserved.
Angular momentum, often represented by the letter L in equations, is a property of an object’s moment of inertia and angular velocity. The moment of inertia, usually represented by the letter I, is a measure of an object’s resistance to changes in rotation. It is a function of the object’s mass and shape. The units of a moment of inertia are the area of mass times, but the exact formula for the moment of inertia depends on the shape of the object. Physics and engineering textbooks often include a graph with formulas for the moment of inertia of common object shapes to aid in calculations.
The angular velocity of an object is measured in radians per second and is usually represented by the Greek letter omega. It is calculated by dividing the component of the velocity vector that is perpendicular to the range of motion by the radius. In practice, the result is often obtained by multiplying the magnitude of the velocity vector by the sine of the angle of the vector and dividing by the magnitude of the radius.
To find the angular momentum of an object, the moment of inertia is multiplied by the angular velocity. Since both are vector quantities, conservation of angular momentum must also involve a vector quantity. Vector multiplication is performed to calculate the angular momentum, L = I*w.
If the object for which angular momentum is calculated is a very small particle, it can be calculated using the equation L = m*v*r. In this equation, m is the mass of the particle, v is the component of the velocity vector that is perpendicular to the beam of motion, and r is the length of the beam. The quantities in this equation are all scalar and a positive or negative sign is used to indicate the direction of rotation.
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