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The formula for the time dilation due to rotation, is given by ?

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^3}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{R_m\,c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{R_M\,c^2}}$$

now, the distance from the axis of rotation $~R_m~$ to the mass m is bigger then the distance from the axis of rotation $~R_M~$ to the mass M

thus the time dilation $$~\Delta t'_m > \Delta t'_M$$

To calculate the effect of time dilation due to rotation for a rotating object with mass m, you need to consider the rotational speed and the distance from the axis of rotation.

The formula for the time dilation due to rotation, is given by ?

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^3}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{R_m\,c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{R_M\,c^2}}$$

now, the distance from the axis of rotation $~R_m~$ to the mass m is bigger then the distance from the axis of rotation $~R_M~$ to the mass M

thus the time dilation $$~\Delta t'_m > \Delta t'_M$$

The formula for the time dilation due to rotation, is given by ?

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^2}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{c^2}}$$

thus if $ ~m < M~$ the time dilation $~\Delta t'_m > \Delta t'_M$

The formula for the time dilation due to rotation, is given by ?

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^3}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{R_m\,c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{R_M\,c^2}}$$

now, the distance from the axis of rotation $~R_m~$ to the mass m is bigger then the distance from the axis of rotation $~R_M~$ to the mass M

thus the time dilation $$~\Delta t'_m > \Delta t'_M$$

The formula for the time dilation due to rotation, is given by:

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^2}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{c^2}}$$

thus if $ ~m < M~$ the time dilation $~\Delta t'_m > \Delta t'_M$

The formula for the time dilation due to rotation, is given by ?

$$ \Delta t'=\Delta t\,\sqrt{1-\frac{4\,G\,J}{c^2\,R^2}}\tag 1$$

where

• $\Delta t~$ is the time interval measured by a distant observer (proper time).
• $\Delta t'~$ is the time interval measured by an observer close to the rotating object.
• G is the gravitational constant.
• J is the angular momentum (spin) of the rotating object.
• R is the distance from the axis of rotation.
• c is the speed of light in vacuum.

applying equation (1) with $~J_m=m\,\omega\,R_m^2~$ you obtain for the mass m

$$\Delta t'_m=\Delta t\,\sqrt{1-\frac{4\,G\,m\,\omega}{c^2}}$$

and for the mass M

$$\Delta t'_M=\Delta t\,\sqrt{1-\frac{4\,G\,M\omega}{c^2}}$$

thus if $ ~m < M~$ the time dilation $~\Delta t'_m > \Delta t'_M$