# Does mass increase as velocity increases?

• oz93666
In summary, the conversation discusses the definition of mass and its different types (relativistic, invariant, inertial, and gravitational). The OP initially defines mass as a measure of an object's ability to attract other masses and resist acceleration, but later realizes that this definition is incorrect in the context of relativity. The conversation also touches on the idea of directional relativistic mass and its relevance to the original definition of mass. The conversation is then closed due to potential moderation issues.
oz93666
First let me see if I understand what mass is ...it's the measure of an objects ability to attract other masses , and also resist acceleration ... the two always come together and define the term "mass" ... there are no subdivisions in the term 'mass' ... no different kinds of mass .

I was brought up to understand that the mass of an object increased with it's speed ... now it seems this was wrong ...

So does the mass of an object increase to infinity at light speed or not?

oz93666 said:
First let me see if I understand what mass is ...it's the measure of an objects ability to attract other masses , and also resist acceleration ... the two always come together and define the term "mass" ... there are no subdivisions in the term 'mass' ... no different kinds of mass .

I was brought up to understand that the mass of an object increased with it's speed ... now it seems this was wrong ...

So does the mass of an object increase to infinity at light speed or not?

No. I know you've been pointed at the FAQ that explains why. Also, you may like to note that with relativistic mass defined as ##m = \gamma m_0##, you do not get ##\vec{F} = m \vec{a}## except where ##\vec{F}## is perpendicular to ##\vec{v}##. For 1D motion you get:

##F = \gamma^3 m_0a = \gamma^2 ma##

This implies also that you have a different relativistic "mass" depending on the direction of the force.

https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

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oz93666 said:
there are no subdivisions in the term 'mass' ... no different kinds of mass .
It would be nice if that were true. Unfortunately there are several kinds of mass. There is relativistic mass, invariant mass, inertial mass, and gravitational mass.

PeroK said:
This implies also that you have a different relativistic "mass" depending on the direction of the force.

No, it implies that relativistic mass and M in F=M·a are different things.

DrStupid said:
No, it implies that relativistic mass and M in F=M·a are different things.

The OP implicitly defined relativistic mass so that ##F = ma##, or a "measure of an object's ability to resist acceleration". The OP would need a directional relativistic mass by that definition.

PeroK said:
The OP implicitly defined relativistic mass so that ##F = ma##, or a "measure of an object's ability to resist acceleration". The OP would need a directional relativistic mass by that definition.

No, he don't. The force required for a specific acceleration at a given velocity is always proportional to mass and relativistic mass, Thus both are a measure of the object's ability to resist acceleration and non of them depend on direction.

He also assumed mass to be "the measure of an objects ability to attract other masses". Your "directional relativistic mass" has nothing to do with this property and is therefore off-topic.

The OP just mixed classical mechanics with relativity. In classical mechanics there is indeed only one kind of mass which is both a measure of gravity and inertia. But this is not the case in relativity.

Thread locked for possible moderation.

Edit: thread reopened after removal of problematic posts

Last edited by a moderator:

## 1. Does mass increase as velocity increases?

According to Einstein's theory of relativity, the mass of an object does indeed increase as its velocity increases. This phenomenon is known as relativistic mass.

## 2. How does mass increase with velocity?

The increase in mass with velocity is described by the equation m = m0 / √(1 - (v^2/c^2)), where m0 is the rest mass of the object, v is the velocity, and c is the speed of light. As the velocity approaches the speed of light, the mass of the object approaches infinity.

## 3. Is this increase in mass significant?

The increase in mass with velocity is significant for objects moving at high speeds, such as particles in particle accelerators. However, for everyday objects, the increase in mass is too small to be measured.

## 4. Does this mean that an object's mass is not constant?

While an object's rest mass is constant, its relativistic mass changes with velocity. This does not violate the law of conservation of mass, as the total energy (including the mass-energy) of the object remains constant.

## 5. How does this affect the behavior of objects at high speeds?

As an object's mass increases with velocity, its inertia also increases, making it more difficult to accelerate. This is why it becomes increasingly difficult to accelerate an object as it approaches the speed of light. Additionally, the increase in mass affects the object's energy and momentum, leading to other interesting effects, such as time dilation and length contraction.

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