A basic doubt (about inertial frames)

[bksree]

Hi
This question is taken from the book Classical mechanics by Gregory.
Please clear this doubt
TIA
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Suppose that a reference frame fixed to the Earth is exactly inertial. Which of the following are then inertial frames ?
A frame fixed to a motor car which is
(i) moving with constant speed around a flat race track
(ii) moving with constant speed along a straight undulating road
(iii) moving with constant speed up a constant gradient
(iv) freewheeling down a hill

Ans (iii). In the other cases, the frame is accelrating or rotating relative to the earth.

The question is :
Why is (ii) not an inertial frame

 

[mikeph]

Undulating = moving up and down. So the car is accelerating up and down.

 

[entphy]

In this case, even if the car manages to keep constant speed on the undulating up and down road, i.e. controlling the engine to cancel the accelerating and decelerating effect of the gravitational field, the car still changes its directions up and down from time to time. Thus, the velocity is not constant since direction changes. Hence, the car in case (ii) cannot be regarded as inertial reference frame.

 

[DaveC426913]

It may help bksree to know that speed is a scalar (distance), whereas velocity is a vector (distance and direction).

"At constant speed" means that the car is making stready progress along the road regardless of how twisty-turny the road is. i.e. the car is doing 60mph on the road.

This is not the same as the car having "constant velocity". Velocity includes direction, so the car's velocity is changing all the time (60mph level, 60mph sloped down, 60mph sloped up, etc.)



Another way to tell that it not inertial is ask imagine yourself in the car and ask if you feel any forces.

The road is undulating (up and down). Do you feel forces lifting you and pushing you? Yes. Thus, it is not inertial.

 

[256bits]

QUOTE=DaveC426913;3425371]

Another way to tell that it not inertial is ask imagine yourself in the car and ask if you feel any forces.

The road is undulating (up and down). Do you feel forces lifting you and pushing you? Yes. Thus, it is not inertial.[/QUOTE]

Consider option iv)
(iv) freewheeling down a hill
One would not feel any force whatsoever in this situation, and if you covered up all the windows so you could not see out, one could not tell if one was in freefall in a gravitaitonal field or in a inertal frame with no forces acting ( or balanced forces ). But of course, look out a window and you cann obviously see that you are accelerating with respect to the earth.

all other choices have a force:
I) has centripetal plus gravity
ii) has gravity plus variable vertical force
ii) has gravity only

Choice v) none of the above
Obviously a trick question.


So one has to go back to the question and analyze it complety.
What the author means by the following statement:
"Suppose that a reference frame fixed to the Earth is exactly inertial. "

In reality:
The Earth is rotating, so no frame on the Earth is inertial.
The Earth has gravitational acceleration so no frame on the Earth is inertial.

The author has disregarded the Earth's rotation and gravitation his "exactly inertial" reference frame.

Thus all of the other posts are as stated do lead to the correct answer iii)