Linear Momentum vs. Angular Momentum: Know the Difference
By Shumaila Saeed || Updated on December 25, 2023
Linear momentum is a measure of an object's translational motion, while angular momentum quantifies its rotational motion.
Key Differences
Linear momentum, denoted as p, is defined as the product of an object's mass m and its velocity v. It represents the quantity of motion an object possesses during linear (straight-line) motion. Linear momentum is a vector quantity, meaning it has both magnitude and direction. It is conserved in an isolated system, where external forces are absent.
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Dec 16, 2023
Angular momentum, denoted as L, is the rotational analogue of linear momentum. It is defined as the product of an object's moment of inertia I and its angular velocity ω. Angular momentum describes the amount of rotational motion an object has and is also a vector quantity. It too is conserved in an isolated system, where external torques are absent.
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Dec 16, 2023
Linear momentum is integral in understanding collision and conservation principles in physics. For example, in a perfectly inelastic collision, the total linear momentum before and after the collision remains constant.
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Dec 16, 2023
Angular momentum plays a crucial role in systems involving rotational dynamics, such as planets orbiting a star or a figure skater spinning. The conservation of angular momentum explains why a figure skater spins faster when they pull their arms in.
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Dec 16, 2023
The formula for linear momentum is p=mv. This relationship implies that a heavier or faster object will have more momentum.
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Dec 16, 2023
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The formula for angular momentum is L=Iω. This indicates that an object's angular momentum depends on its distribution of mass (moment of inertia) and its rate of rotation.
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Dec 16, 2023
Comparison Chart
Definition
Product of mass and velocity
Product of moment of inertia and angular velocity
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Conservation Law
Conserved in absence of external forces
Conserved in absence of external torques
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Dec 16, 2023
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Example
A moving car has linear momentum
A spinning top has angular momentum
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Linear Momentum and Angular Momentum Definitions
Linear Momentum
Linear momentum reflects how difficult it is to stop a moving object.
A fast-moving hockey puck has enough linear momentum to be hard to stop.
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Dec 10, 2023
Angular Momentum
Angular momentum depends on the distribution of an object's mass and its rotation.
Earth's angular momentum affects its day-night cycle.
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Dec 10, 2023
Linear Momentum
Linear momentum is conserved in an isolated system.
In space, an astronaut's linear momentum remains constant unless acted upon.
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Dec 10, 2023
Angular Momentum
Angular momentum is conserved in a system with no external torque.
A spinning top maintains its angular momentum until external forces act on it.
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Dec 10, 2023
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Linear Momentum
Linear momentum quantifies the motion of a body in a straight line.
The linear momentum of a bullet is a key factor in its impact.
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Dec 10, 2023
Angular Momentum
Angular momentum is a vector quantity, associated with rotational motion.
The angular momentum of a rotating fan dictates its speed and direction of rotation.
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Dec 10, 2023
Linear Momentum
Linear momentum is the product of an object's mass and velocity.
A train moving at high speed has significant linear momentum.
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Dec 10, 2023
Angular Momentum
Angular momentum is the rotational equivalent of linear momentum.
A spinning ice skater maintains her angular momentum unless she changes her body position.
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Dec 10, 2023
Linear Momentum
Linear momentum is a vector quantity, showing both magnitude and direction of motion.
The linear momentum of a river flowing northwards is directed north.
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Dec 10, 2023
Angular Momentum
Angular momentum is the product of an object's moment of inertia and its angular velocity.
A discus thrower imparts angular momentum to the discus during the throw.
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Dec 10, 2023
Repeatedly Asked Queries
What is an example of angular momentum conservation?
A figure skater spinning faster when they pull in their arms.
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Dec 16, 2023
What is linear momentum?
Linear momentum is the product of an object's mass and velocity.
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Dec 16, 2023
What is the unit of linear momentum?
It's measured in kilogram meters per second (kg·m/s).
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Dec 16, 2023
How is angular momentum defined?
Angular momentum is the product of an object's moment of inertia and angular velocity.
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Dec 16, 2023
What does the conservation of linear momentum mean?
It means the total linear momentum of a system remains constant if no external forces act on it.
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Dec 16, 2023
Does angular momentum depend on the axis of rotation?
Yes, it varies with different axes of rotation.
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Dec 16, 2023
How does angular momentum affect planetary motion?
It explains why planets continue to orbit the Sun without slowing down.
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Dec 16, 2023
What factors affect angular momentum?
The distribution of mass (moment of inertia) and the speed of rotation.
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Dec 16, 2023
Can angular momentum exist in a system with a single point mass?
No, it requires a distribution of mass around an axis.
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Dec 16, 2023
How is linear momentum related to Newton’s laws?
It's directly related to Newton's second law, linking force and change in momentum.
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Dec 16, 2023
Is linear momentum a scalar or vector quantity?
It's a vector quantity, having both magnitude and direction.
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Dec 16, 2023
Can linear momentum change direction?
Yes, if an external force changes the object's velocity direction.
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Dec 16, 2023
Can angular momentum be transferred?
Yes, through collisions or connecting objects, like dancers spinning together.
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Dec 16, 2023
What role does linear momentum play in collisions?
It helps determine the outcome and energy transfer during collisions.
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Dec 16, 2023
What unit is used for angular momentum?
The unit is kilogram square meters per second (kg·m²/s).
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Dec 16, 2023
What happens to angular momentum when an ice skater opens their arms?
It decreases, causing the skater to spin slower.
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Dec 16, 2023
How do linear and angular momentum differ in terms of their physical concept?
Linear momentum relates to straight-line motion, while angular momentum deals with rotational motion.
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Dec 16, 2023
Is it possible to have high linear momentum with low speed?
Yes, if the object has a large mass.
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Dec 16, 2023
How is torque related to angular momentum?
Torque is the rotational analogue of force and affects the change in angular momentum.
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Dec 16, 2023
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About Author
Written by
Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.
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