What is Angular motion ?
In Physics, there are various formulas for calculating linear velocity, and displacement and for calculating the angular momentum you can find equivalent formulae. Here we will be discussing the relationship between angular motion and linear motion. The angular motion is the motion where the body moves along the curved path at a constant and consistent angular velocity. An example is when a runner travels along the circular path or the automobile that goes around the curve. One of the common issues here is calculating centrifugal forces and determining its impact on the motion of the object.
Angular velocity
There are two categories of the angular velocity: Spin angular velocity and orbital angular velocity. The spin angular velocity refers to the speed of rotation of an object or rigid body, with respect to its axis of rotation. The spin velocity of the angular object is independent of choice of origin, in contrast to the theory for orbital angular velocity.
In kinematics, we have studied the motion through a straight line and the concept of velocity or displacement and acceleration. In 2D kinematics, we deal with the concept of motion within two dimensions. The projectile motion is the special scenario for the 2D kinematics where the object is projected in the air. This object is subjected to gravitational force and then it lands a distance away. Here we will cover some of the situations where an object doesn’t land but moves in the curved path.
Have we ever wondered that How fast an object is rotating? We define angular velocity as ω -as the rate of change of the angle. In symbols, this is written as:
ω=Δθ/Δt
ω=Δθ/Δt
Here an angular rotation that is Δθ takes place in a time Δt. The greater the rotation angles in a given amount of time the greater the angular velocity is there. The units which are for angular velocity are radians per second which are rad/s.
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Angular velocity denoted as ω is analogous to linear velocity that is v. To get a very precise relationship between the linear velocity and the angular velocity, we shall again consider a pit on the rotating CD. This pit moves as an arc length that is Δs in a time that is Δt, and so it has a linear velocity which is written as:
v=Δs/Δt
Rotational angles
The rotational angle involves an object that rotates about its own axis at the time of some other axis - for instance, a compact disk or a CD rotates about its centre - then each point within the object starts following a path that has the circular arc. You can visualise it as a line from the CD’s centre to the edge of the CD. The angle of rotation is essentially representing the amount of rotation and it is considered analogous to linear distance. The angular velocity can be defined as the rate of change in the angle. We hereby define the angle of rotation as Δθ which is said to be the ratio of the arc length to the radius of curvature that is:
Δθ=Δvr
Types and explanation of different angular motion
Particles Which are Three Dimension
In the space of three-dimensional particles, we again have the position vector that is r of a moving particle. Here if we notice as there are two directions that are perpendicular in nature to any plane which is an additional condition is necessary to uniquely specify the direction of the angular velocity which is conventionally the rule of right-hand used.
Vector of angular velocity for the rigid body
If you have a rotating frame of three unit vectors then the coordinates of all the three should have the same angular speed at each of the points. In such frames, each vector can be regarded as the moving particle having a constant scalar radius. The rotating frame always tends to appear within the context of rigid bodies and specialised custom tools have been developed for this.
Hence article explained what is angular motion and angular velocity. Students will develop a basic understanding of angular velocity after going through the article.
FAQs on Angular Motion
1. What is angular motion as explained in Physics?
Angular motion, also known as rotational motion, describes the movement of an object around a fixed point or axis. Unlike linear motion where an object travels in a straight line, here the object follows a circular or curved path. Its position is measured by the angle of rotation (θ) it sweeps out from a reference line.
2. What are some common real-world examples of angular motion?
Angular motion is observed everywhere around us. Some clear examples include:
- The blades of a ceiling fan spinning around its central hub.
- The Earth rotating on its own axis, which causes day and night.
- The wheels of a moving car rotating around their axles.
- An ice skater spinning on the spot.
- A planet, like Mars, revolving in its orbit around the Sun.
3. How does angular motion fundamentally differ from linear motion?
The primary differences between linear and angular motion lie in the variables used to describe them. As per the CBSE 2025-26 syllabus, understanding these analogies is key:
- Path: Linear motion is along a straight line, while angular motion occurs along a circular path.
- Displacement: In linear motion, we measure linear displacement (s), while in angular motion, we measure angular displacement (θ).
- Velocity: Linear motion has linear velocity (v), the rate of change of displacement. Angular motion has angular velocity (ω), the rate of change of the angle.
- Inertia: Resistance to a change in linear motion is mass (m). Resistance to a change in rotational motion is called the moment of inertia (I).
4. What are the key equations that describe angular motion with constant angular acceleration?
The kinematic equations for angular motion are direct analogues of the linear motion equations. The three fundamental equations are:
- ω = ω₀ + αt (Analogous to v = u + at)
- θ = ω₀t + ½αt² (Analogous to s = ut + ½at²)
- ω² = ω₀² + 2αθ (Analogous to v² = u² + 2as)
5. Why is angular velocity considered a vector quantity, and how is its direction determined?
Angular velocity (ω) is a vector because it has both a magnitude (how fast an object rotates) and a direction (the axis about which it rotates). To fully describe rotation in three-dimensional space, the direction is essential. Its direction is determined by the right-hand rule: if you curl the fingers of your right hand in the direction of the object's rotation, your extended thumb points along the axis of rotation, which is the direction of the angular velocity vector.
6. An object in uniform circular motion has a constant speed but is still accelerating. How can this be explained?
This is a classic concept in physics. While the object's speed (a scalar quantity) is constant, its velocity (a vector quantity) is continuously changing because its direction of motion is always changing. Since acceleration is defined as the rate of change of velocity, any change—whether in magnitude or direction—results in acceleration. This specific acceleration, called centripetal acceleration, is always directed towards the centre of the circular path and is responsible for keeping the object in its curved trajectory.
7. How does the concept of torque cause a change in an object's angular motion?
Torque (τ) is the rotational equivalent of force. Just as a net force causes a change in linear motion (linear acceleration), a net torque causes a change in angular motion, which is called angular acceleration (α). This relationship is defined by the rotational version of Newton's second law: τ = Iα, where 'I' is the moment of inertia. Therefore, to make an object start spinning, stop spinning, or change its rate of rotation, a net external torque must be applied.
8. What is the physical significance of the moment of inertia in rotational dynamics?
The moment of inertia (I) represents an object's inherent resistance to changes in its state of rotation. Its significance lies in the fact that it depends not just on the object's mass, but crucially on how that mass is distributed relative to the axis of rotation. For example, a hollow hoop and a solid disk of the same mass and radius will have different moments of inertia. The hoop, with its mass concentrated far from the centre, has a higher moment of inertia and is therefore harder to start or stop rotating than the solid disk.
9. What is the difference between spin angular motion and orbital angular motion?
Both are types of angular motion, but they differ based on the location of the axis of rotation:
- Spin Angular Motion refers to an object's rotation about an axis that passes through its own body or centre of mass. A classic example is the Earth spinning on its axis to create day and night.
- Orbital Angular Motion describes an object's revolution around an external axis or point. For instance, the Earth revolving around the Sun is an example of orbital motion. An object can exhibit both simultaneously.
10. How is the relationship between linear and angular velocity defined for a point on a rotating object?
The relationship between the tangential linear velocity (v) of a specific point on a rotating body and its overall angular velocity (ω) is given by the formula v = ωr. In this equation, 'r' is the perpendicular distance of the point from the axis of rotation. This means that for a rigid body rotating at a constant angular velocity, points farther from the axis (larger 'r') move at a higher linear speed than points closer to the axis.
