Angular Velocity linear Velocity

In physics, angular velocity, also known as rotational velocity or angular frequency vector, is a vector measure of rotation rate that describes how quickly an object spins or revolves relative to another point, that is how quickly the angular position or direction of an object changes over time. In simple terms we can say angular velocity has an angle per unit time dimension.

The rate of change in position over time is referred to as velocity. The velocity of an object along a straight line is called linear velocity, whereas angular velocity refers to how much an object spins, rotates, or turns. Linear velocity is measured in m/s .

Velocity

The rate of change of an object’s position in relation to a frame of reference is its velocity, which is a function of time. The meaning of an object’s speed and direction of travel (e.g. 60 km/hr north) is similar to velocity. In kinematics, the branch of classical mechanics that gives the motion of bodies, velocity is a conceptual notion. Velocity is a physical vector quantity that defines magnitude and direction. Speed is a scalar quantity and it is a coherent derived unit whose quantity is measured in metres per second (m/s) [SI (metric system)]. Acceleration can be defined when there is a change in speed with respect to time.

Average velocity

Velocity can be defined as the change of distance with respect to time, which is also referred to as instantaneous velocity to underline the distinction from average velocity. The average velocity of an item, defined as the constant velocity that causes the same net displacement as a variable. velocity in the same time interval, v(t)over some time period t, may be required. The following formula can be used to compute average velocity:

v =∆x∆t

The average velocity of an object is always less than or equal to its average speed. This can be seen by observing that, whereas distance is always strictly rising, displacement can change direction as well as increase or decrease in magnitude.

Linear velocity

The speed at which the position of an object travelling along a straight path is known as linear velocity. Any moving item has a linear velocity. This parameter is quite common in everyday life because any moving object has a linear velocity.  For example, when a person walks, drives, runs, or rides a bike, this is a linear velocity.

An object may be moving at a constant speed along a straight path. When this occurs, the item is said to be travelling at a constant linear velocity.

Linear velocity formula

Each point along a radius line travelling with an angular velocity of has a distinct linear velocity (v) depending on its distance r from the centre of rotation. As r gets bigger, also vwill be larger. The formula is given as 

v=ω×r

This expression gives the linear velocity in units of distance over time, as expected, because radians are dimensionless units. You can easily determine the linear velocity of the rotating point if you know the frequency of rotation. It’s as follows: 

v=(2πf)×r

v=(2πp)×r

Angular velocity

Angular velocity is the velocity associated with rigid bodies when they rotate around a fixed axis. The rotation rate of an object is measured in angular velocity, which is a vector measure of how fast it rotates or revolves in relation to another point. To know about angular velocity, take an example of a windmill, a windmill is a rotating rigid body with a fixed axis. When the blades of a windmill revolve around an axis that passes through the rotor, it shows rotational motion. We also call angular velocity as the rotational velocity. 

Angular velocity formula

A line from the object to the centre of the circle follows an arc on the circle while spreading out an angle at the centre of the circle when an object moves on a circular path from point A to point B. The value of the angle (∅ ) swept out as the object travels from A to B is given by if the length of the arc AB is denoted by the  s and the distance from the object to the centre of the circle is represented by r  the formula will be:

∅= sr 

In general, the average angular velocity of a rotating object ( w) is calculated by measuring the time ( t ) it takes for the radius line to sweep out any angle and applying the formula:

ω= ∅t (rad/s)

Here ∅ is measured in radians. One radian =57.3 degree.

Difference between linear and angular velocity

Angular Velocity: The speed at which the angular location of a rotating body changes is known as angular velocity. The angular velocity of a particle is along the axis of a circle when an object moves in a circular motion. The angular velocity does not change. It is represented by .

Linear velocity: When an object moves along a straight route, linear velocity is defined as the rate of change of displacement with respect to time. A particle’s linear velocity is along the circumference of a circle when an object moves in a circular motion. Every point on the circle has a different linear velocity. It is represented by v.

Conclusion

Angular velocity, also known as rotational velocity or angular frequency vector, is a vector measure of rotation rate that describes how quickly an object spins or revolves relative to another point. The rate of change in position over time is referred to as velocity. Velocity is defined as the rate of change in distance with respect to time which is also referred to as instantaneous velocity to underline the distinction from average velocity. The speed at which the position of an object travelling along a straight path is known as linear velocity. Any moving item has a linear velocity. The angular velocity does not change. It is represented by . Linear velocity is represented by v.