Time Dilation - Angular Momentum - Mass

In summary, the conversation discusses the concept of conservation of angular momentum and whether it is also invariant. It is clarified that angular momentum is conserved but not necessarily invariant, unlike linear momentum.
  • #1
kmarinas86
979
1
Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?
 
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  • #2
kmarinas86 said:
Angular momentum must be conserved. Does that mean that if a particle travels at relative velocity to an observer that the decrease in apparent spin rate will be offset by the increase in mass causing the angular momentum to be constant?

I think you're confusing the words "conserved" and "invariant". When a quantity is conserved, it maintains the same value at different times in the same reference frame. When a quantity is invariant, it has the same value when measured from different reference frames. Angular momentum is conserved but I don't think it's necessarily invariant. Certainly linear momentum is not invariant, although it is conserved.
 
  • #3


Yes, that is correct. According to the principle of conservation of angular momentum, the total angular momentum of a system must remain constant. This means that any changes in the spin rate or mass of a particle will be offset by corresponding changes in the other variable, in order to maintain a constant angular momentum.

In the case of time dilation, the apparent spin rate of a particle will decrease as it travels at a high relative velocity to an observer. However, this decrease in spin rate will be offset by an increase in the particle's mass due to its high velocity. This increase in mass will result in a higher angular momentum, balancing out the decrease in spin rate and keeping the total angular momentum constant.

Therefore, the conservation of angular momentum plays a crucial role in understanding the effects of time dilation and the relationship between angular momentum, velocity, and mass.
 

1. What is time dilation?

Time dilation is a phenomenon in which time appears to move slower for an observer moving at a high velocity compared to an observer at rest. This is a result of the theory of relativity, which states that time is relative and can be affected by factors such as speed and gravity.

2. How does angular momentum affect an object's motion?

Angular momentum is a measure of an object's rotational motion. It is the product of an object's moment of inertia and its angular velocity. An object with a high angular momentum will continue to rotate at the same speed unless acted upon by an external force.

3. Can mass affect an object's speed?

According to the theory of relativity, as an object's speed approaches the speed of light, its mass increases. This increase in mass makes it more difficult for the object to accelerate and ultimately prevents it from reaching the speed of light.

4. How does time dilation impact space travel?

Time dilation can have a significant impact on space travel, especially at high speeds. As a spacecraft travels closer to the speed of light, time will appear to pass slower for the astronauts onboard compared to those on Earth. This means that the astronauts may experience less time passing, allowing them to travel further in the same amount of time from their perspective.

5. Is time dilation just a theory or has it been proven?

Time dilation has been proven through experiments and observations, particularly in high-speed particle accelerators and in studies of atomic clocks in space. The effects of time dilation have been confirmed by multiple experiments and are a key component of the theory of relativity.

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