Why is angular momentum conserved but not linear?

Answer 1

A rotating object will continue to rotate on its axis if it is free from any external torque; angular momentum is a measure of this tendency. Although angular and linear momentum are not directly related, both are conserved.

Since both angular and linear momentum have magnitudes and directions associated with them, they are vector quantities. Linear momentum is an object's tendency to continue in one direction. An object traveling in a given direction at a certain velocity will continue to do so until acted upon by an external force (Newton's first law of motion).

The formula for angular momentum is:

#L=r * mv_"tangential"#
where #L# is the angular momentum, #r# is the radius of the mass relative to the axis of rotation, m is the mass of the object, and #v_"tangential"# is the velocity vector of the mass tangent to the radius of rotation

Given linear momentum, we have:

#p=mv#
where #p# is the linear momentum of the object, #m# is the mass, and #v# is the velocity of the object in the direction of travel

Spinning in a chair with weights in each hand is a common example of the conservation of angular momentum in the physics classroom. The student will rotate faster when the weights are brought in (because the radius is smaller), but the chair will also rotate more slowly when the student extends his hands.

In collision mechanics, two objects of the same mass colliding and one starting at rest provides a common example of the conservation of linear momentum: in a perfectly inelastic collision, the final velocity of the system will be exactly 1/2 of the velocity of the mass that was moving initially.

#p_m1+p_m2=p_m1m2# #m_1v_1+m_2v_2=(m_1+m_2)v_12#
Since #m_2# started at rest, #v_2=0#, and we are assuming #m_1=m_2#:
#m_1v_1=2m_1v_12# #v_12=1/2v_1#
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Answer 2

Angular momentum is conserved due to the rotational symmetry of physical laws, as described by Noether's theorem. Linear momentum is not conserved in all situations because external forces can act on a system, changing its linear momentum.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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