I have been considering mph , and I do not understand how mph can be true , when a curvature velocity running parallel to a linear velocity at the same mph travels slower compared to the linear.

 

 

Can someone explain how this works?

Edited October 11, 201411 yr by Relative

miles per hour is a speed. As is meters per second, or furlongs per fortnight. distance/time. It has nothing to do with curvature.

Two cars, both doing 50 miles per hour.

 

One is going around and around an oval. One driving from Paris to Berlin.

 

So what? Different paths: both are travelling at the same speed relative to the road. One seems to "get somewhere", the other doesn't.

 

Yes, a tunnel from Paris to Berlin might allow an even straighter path (avoiding curve of Earth surface) but 50 mph is still 50 mph.

I have been considering mph , and I do not understand how mph can be true , when a curvature velocity running parallel to a linear velocity at the same mph travels slower compared to the linear.

 

miles.jpg

 

Can someone explain how this works?

It is the difference between "distance" and "displacement". Displacement is the straight line separation and direction, while distance is the length of the path taken. If you drive a straight line between A and B, distance and displacement are equal. If you drive a curved path, they are not.

It is also the difference between speed and velocity.

Miles per hr are generally measured as distance over time. It is a speed with no regard to direction. Velocity has both a speed and direction component.

 

So while the car driving the curved and straight paths have the same speeds in MPH, they do have different velocities, the curved path car changes direction as it drives.

 

If you average out the changing velocity of the curved path you get a straight line average velocity along the line of displacement (displacement/time), which is less than the same average velocity for the straight line car.

 

IOW, the while the speeds (distance/time) of the cars remain the same , the average velocities (displacement/time) are not the same. So it just depends on which you are concerned about. For example, if I ask my GPS to find the gas stations, it will list them giving the distances as a straight line displacement (5 miles SW, etc.) However if I then have it calculate the route, it gives me the driving driving distance and driving time based on that distance.

It is the difference between "distance" and "displacement". Displacement is the straight line separation and direction, while distance is the length of the path taken. If you drive a straight line between A and B, distance and displacement are equal. If you drive a curved path, they are not.

It is also the difference between speed and velocity.

Miles per hr are generally measured as distance over time. It is a speed with no regard to direction. Velocity has both a speed and direction component.

 

So while the car driving the curved and straight paths have the same speeds in MPH, they do have different velocities, the curved path car changes direction as it drives.

 

If you average out the changing velocity of the curved path you get a straight line average velocity along the line of displacement (displacement/time), whichT is less than the same average velocity for the straight line car.

 

IOW, the while the speeds (distance/time) of the cars remain the same , the average velocities (displacement/time) are not the same. So it just depends on which you are concerned about. For example, if I ask my GPS to find the gas stations, it will list them giving the distances as a straight line displacement (5 miles SW, etc.) However if I then have it calculate the route, it gives me the driving driving distance and driving time based on that distance.

thank you a very good explanation, I now know it is called displacement, and one final question, does this have anything to do with time dilation?

Edited October 12, 201411 yr by Relative

thank you a very good explanation, I now know it is called displacement, and one final question, does this have anything to do with time dilation?

 

Not really, no. This discussion has been entirely non-relativistic so far.