In classical physics, angular velocity (rotational velocity) is the vector measure of rotation rate. It indicates how fast a body revolves or rotates relative to another point. It can also be defined as how fast a body’s angular orientation or position varies with time. There are two forms of angular velocity in classical mechanics. Orbital angular velocity shows how fast a point body revolves around a constant origin. It is the time rate of change of the body’s angular position with respect to the origin. Spin angular velocity shows how fast a compact body rotates with respect to its centre of rotation. It doesn’t depend on the choice of origin. In the case of orbital angular velocity, it directly depends on the choice of origin.
Generally, angular velocity possesses a dimension of angle per unit. In this case, the quantity of angle replaces the quantity of linear velocity with time. The SI unit of angular velocity is radians per second. As a radian is a dimensionless quantity, the unit can be denoted as s-1. Angular velocity is generally denoted by the symbol omega ‘ω’. Positive angular velocity represents a counter-clockwise rotation, and negative represents a clockwise rotation.
The video explains the fundamental concepts of angular velocity.
Angular velocity is fundamentally a pseudovector. Its magnitude shows the angular speed, the rate at which a body revolves or rotates and the direction perpendicular to the instantaneous rotation plane of angular displacement. The right-hand rule usually gives the direction of angular velocity. The angular velocity direction is challenging to track as a point on a rotating body constantly varies the direction. The axis of the rotating body is the point where the body has a constant direction. With the help of axis rotation, the angular velocity direction can be found by the right-hand rule.
Average Angular Velocity
The average angular velocity is the ratio of the angular displacement to its time interval.
Instantaneous Angular Velocity
The instantaneous angular velocity is the limit of the average angular velocity as the time interval reduces to zero.
Important Angular Velocity Questions with Answers
1) What is meant by angular velocity?
Angular velocity (rotational velocity) is the vector measure of rotation rate. It indicates how fast a body revolves or rotates relative to another point. It can also be defined as how fast a body’s angular orientation or position varies with time.
2) What are the two forms of angular velocity?
There are two forms of angular velocity in classical mechanics. Orbital angular velocity shows how fast a point body revolves around a constant origin. It is the time rate of change of the body’s angular position with respect to the origin. Spin angular velocity shows how fast a compact body rotates with respect to its centre of rotation. It doesn’t depend on the choice of origin. In the case of orbital angular velocity, it directly depends on the choice of origin.
3) What are measuring units of angular velocity?
Generally, angular velocity possesses a dimension of angle per unit. In this case, the quantity of angle replaces the quantity of linear velocity with time. The SI unit of angular velocity is radians per second. As a radian is a dimensionless quantity, the unit can be denoted as s-1. Angular velocity is generally denoted by the symbol omega ‘ω’. Positive angular velocity represents a counter-clockwise rotation, and negative represents a clockwise rotation.
4) Explain the characteristics of angular velocity.
Angular velocity is fundamentally a pseudovector. Its magnitude shows the angular speed, which is the rate at which a body revolves or rotates and the direction perpendicular to the instantaneous rotation plane or angular displacement. The right-hand rule usually gives the direction of angular velocity. The angular velocity direction is challenging to track as a point on a rotating body constantly varies the direction. The axis of the rotating body is the point where the body has a constant direction. With the help of axis rotation, the right-hand rule can find the angular velocity direction.
5) What is meant by average angular velocity?
The average angular velocity is the ratio of the angular displacement to its time interval.
6) What is meant by instantaneous angular velocity?
The instantaneous angular velocity is the limit of the average angular velocity as the time interval reduces to zero.
7) _____ angular velocity represents a counter-clockwise rotation.
Answer: Positive
Explanation: Positive angular velocity represents a counter-clockwise rotation.
8) _____ velocity is generally denoted by the symbol omega ‘ω’.
Answer: omega ‘ω’
Explanation: Angular velocity is generally denoted by the omega ‘ω’.
9) What is the dimensional formula of angular velocity?
Answer: The dimensional formula of angular velocity is [M0 L0 T-1].
10) What is the direction of angular velocity?
Answer: The direction of angular velocity is perpendicular to the plane of rotation.
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Practice Questions
1) What is angular speed?
2) What is meant by angular momentum?
3) What is meant by angular acceleration?
4) What is the angular velocity of the Earth’s rotation?
5) What is the difference between angular velocity and linear velocity?
6) What is the right-hand rule?
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