# Inertial reference frame

## Main Question or Discussion Point

does an object with constant acceleration follow Newton's laws? with constant velocity? a stationary object?

i think the last two are true, but I'm confused whether a constant acceleration (m/s/s) of whatever still applies to an inertial frame or is a noninertial frame?

because in a sample problem it asks to find the acceleration of a puck given the mass and force. the answer yield an acceleration (m/s/s). does that refer to the acceleration that causes it to initially move or to continue to accelerate during motion (like after 1s it would be 9.8m/s and after 2s it would be 19.6m/s)

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Dale
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I think you are mixing up a couple of basic ideas, so I apologize in advance if this sounds a little pedantic.

A reference frame is simply a coordinate system. Its only purpose is to assign numbers to points in space and time which allows us to describe motion mathematically. So, if I say that the position of some object is r(t)=3t it is meaningless unless I have defined the coordinate system or reference frame. Often in physics problems this definition is either done implicitly or it is left to the student.

Strictly speaking velocity and acceleration are mathematical quantities, not physical ones. Velocity is the first derivative of your position and acceleration is the second derivative of position, but the position is defined mathematically by your choice of reference frame.

There are two special kinds of reference frames that are particularly useful in physics. One is called a "rest frame". That is a coordinate system in which some object is at rest, usually at the origin. The position of all other objects are defined with respect to the rest object. However, there is no need to put any object at rest in a given reference frame, you can arrange your coordinate system to your preferences. The only reason to ever use a rest frame is to simplify the math.

The other important kind is called an "inertial frame". That is a coordinate system where Newton's laws are valid. In an inertial frame an object experiencing no force will have no acceleration (second derivative of position is 0). If a reference frame is not inertial then we have to add ficticious forces to "fix" Newton's laws. For example, if we are in a spinning space station then when we let go of a ball it would be experiencing no force and so according to Newton it does not accelerate. However, if we were analyzing the ball's motion in the rest frame of the space station the ball would have a non-zero second derivative as it "falls" to the floor (f=0 a=r''(t)!=0 so Newton's laws do not hold). We would have to use a ficticious force to "fix" Newton's laws. The rest frame of the space station is therefore not an inertial frame.

So, back to your problem. Newton's laws hold in an intertial reference frame, e.g. the rest frame of the ice. If a hockey puck continues to experience a force then it will continue to accelerate in that frame since it is an inertial frame.

If we were to choose a different frame, e.g. the rest frame of the hockey puck, then we would have to "fix" Newton's laws with a ficticious force. This ficticious force would cause the ice to accelerate and would exactly balance the force applied to the puck in order to cause the puck to remain stationary in its rest frame. The rest frame of the puck is not an inertial frame.

Doc Al
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does an object with constant acceleration follow Newton's laws? with constant velocity? a stationary object?
Yes to all three.

i think the last two are true, but I'm confused whether a constant acceleration (m/s/s) of whatever still applies to an inertial frame or is a noninertial frame?
If an object is accelerating, then Newton's laws certainly apply when viewing the object's motion from an inertial frame. (After all, Newton's 2nd law tells you how to find the acceleration given force and mass.) If you view motion from an accelerating frame (very useful in some cases), Newton's 2nd law must be modified. I recommend that you not worry about using non-inertial frames at this point.

because in a sample problem it asks to find the acceleration of a puck given the mass and force. the answer yield an acceleration (m/s/s). does that refer to the acceleration that causes it to initially move or to continue to accelerate during motion (like after 1s it would be 9.8m/s and after 2s it would be 19.6m/s)
If the force is constantly applied, then the puck's acceleration will be constant as well. F = ma applies at every instant.

So when do Newton's laws NOT apply (besides in quantum physics or light speed)

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Dale
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Whenever you are doing the analysis in a non-inertial reference frame. (Not that the physics doesn't work, just the math doesn't work without a bunch of "tweaking")