** Angular Velocity vs Linear Velocity
**

Angular velocity and linear velocity are two forms of velocity, which are applied in a verity of fields. This article addresses the definitions, similarities and differences between linear velocity and angular velocity.

**Linear Velocity**

Linear velocity is defined as the rate of change of displacement between an object and a fixed point. Mathematically speaking, velocity equals dx/dt (read as d, dt x) according to the theories of calculus. It is also denoted in ẋ. Linear velocity is a vector quantity. Linear velocity has the direction of instantaneous movement. Velocity is a relativistic variant, which means the laws of relativity must be applied for velocities compatible with the speed of light. Relative velocity is the velocity of an object relative to another object. In the vector form, this is written as V̰_{A rel B} = V̰_{A} – V̰_{B}. V̰_{rel} is the velocity of object “A” relative to object “B”. Usually a velocity triangle or a velocity parallelogram is used to calculate relative velocity between two objects. Velocity triangle theory states that if V_{A rel Earth} and V_{Earth rel B} are indicated in two sides of a triangle proportional to the magnitude and direction, the third line indicates the direction and magnitude of the relative velocity. Linear velocity is measured in meters per second. The definition of the linear velocity can also be taken as the displacement of the object at a unit time. The magnitude of the linear velocity alone shows the speed of the object.

**Angular Velocity**

Angular velocity is an event discussed in the angular motion. Motions like blades of a rotating fan or a running wheel have angular motion. For the angular motion, an angle drawn radial is used. One side of this angle moves with the object as the other remains still with respect to earth. The angle is known as angular displacement. The rate of change of angular displacement is known as angular velocity and rate of change of angular velocity is known as the angular acceleration. The unit of angular velocity is radians per second, or can be also expressed in revolutions per second. A change in the angular velocity of an object requires external net torque acting upon the system. Another property discussed with the angular velocity is the angular momentum. Angular momentum is equal to the product of the moment of inertial of the object about the rotational axis and the angular velocity. The rotational kinetic energy of the system is equal to the product of the moment of inertia and angular velocity squared and divided by two. Angular velocity is the proper quantity that gives us the impression how fast an object is revolving. This is usually denoted by ω.

• A force is always required to keep an angular velocity, but a constant linear velocity does not require a force. • Angular velocity multiplied by the radius of movement yields the instantaneous linear velocity of the object. • Linear velocity is measured in meters per second, while angular velocity is measured in radians per second. |

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