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Difference Between Linear Momentum and Angular Momentum

Linear Momentum vs Angular Momentum

Angular momentum and linear momentum are two very important concepts in mechanics. These two concepts play a vital role in most of the fields in dynamics. This article will try to compare and contrast what linear momentum and angular momentum are, their definitions, similarities and finally the differences.

What is Linear Momentum?

Linear momentum is a very important property of a moving object. The linear momentum is defined to an object moving on a direct path. The momentum of an object is equal to the mass of the object multiplied by the velocity of the object. Since the mass is a scalar, the linear momentum is also a vector, which has the same direction as the velocity. One of the most important laws regarding momentum is Newton’s second law of motion. It states that the net force acting on an object is equal to the rate of change of momentum. Since mass is a constant on non-relativistic mechanics, the rate of change of linear momentum is equal to mass multiplied by the acceleration of the object. The most important derivation from this law is the linear momentum conservation law. This states that if the net force on a system is zero the total linear momentum of the system remains constant. Linear momentum is conserved even in relativistic scales. It must be noted that the linear momentum is dependent on both the mass of the object and the space-time coordinate change of the object.

What is Angular Momentum?

Angular momentum is defined to an object with angular motion. To define the angular momentum one must first know what the moment of inertia is. The moment of inertia of an object is a property that depends on both the mass of the object, and the mass distribution from the place the moment of inertia is measured. If the total mass is distributed close to the rotational axis, the moment of inertia is lower about that axis. If the mass is spread out far from the axis, the moment of inertia is higher. Angular momentum of an object is the product of the moment of inertia and the angular velocity of the object. Angular velocity is a vector. The direction of the angular velocity is taken by the right hand corkscrew law. Since moment of inertia is a scalar, angular momentum is a vector, with a direction perpendicular to the plane of rotation decided by the right hand corkscrew rule. To change the angular momentum of a system an external torque must be applied. The rate of change of angular momentum is proportional to the applied torque. If no external torque is applied, the angular momentum of a closed system is conserved.

What is the difference between linear momentum and angular momentum?

• Linear momentum is measured in kgm/s while the angular momentum is measured in kgm2rad/s.

• Linear momentum is parallel to the motion while angular momentum is normal to the motion.

• A torque is required to change the angular momentum but a force is required to change linear momentum.


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