# A little confusion on reference frames

1. Oct 5, 2014

### elusiveshame

In college physics 1, I think I'm confusing myself on reference frames, and would like for one of you significantly smarter persons to let me know if I'm on the right path with understanding it, and if not, could point me in the right direction :)

We're just beginning inertia and momentum in both of my classes (physics 1 and mechanics), and the subject of reference frames are starting to become more frequently talked about.

In the book (Physics for scientists & engineers, Giancoli, 4th edition), it states that Newtons first 2 laws are only relevant in the inertial reference frames and not in noninertial reference frames, and gives an example of a cup sitting on a dashboard is outside of your inertial reference frame from the cars.

What does that mean? Does that mean if we were to calculate the sliding of the cup, it would require its own set of variables outside of the scope of the cars, and because from our perspective, it's just sitting there, but from the cups perspective, it's moving with a constant velocity? Wouldn't that be centripetal force?

2. Oct 5, 2014

### bistan

Think of the Earth itself. If you stand still on the Earth, are you really standing still, or are you moving at an angular velocity of $$7.2921159 × 10^{-5} \frac{radians}{second}$$ (the angular velocity of the earth)?

The velocity of the object in the inertial reference frame would equal the velocity of the object in the accelerated reference frame plus the velocity of the accelerated frame with respect to the inertial frame. As in:
$$v_{object/inertialframe} = v_{acceleratedframe/inertialframe} + v_{object/acceleratedframe}$$

Think of it like this: Let's say the earth doesn't move at all or is moving at constant velocity (inertial reference frame). You're standing completely still (inertial reference frame) on the side of the road. Take the positive x direction to be on your right. Suddenly, a bus flies by you from left to right at what you say is 30 m/s, and a guy on rollerblades starts rolling from the back to the front of the bus at 2m/s according to the people in the bus. What's the velocity that you observe of the guy on rollerblades?

It's gotta be 32m/s, since his velocity with respect to the bus is 2m/s, and the velocity of the bus in relation to you is 30m/s. The velocity of the guy on rollerblades according to you has to be the addition of these two velocities.

Last edited: Oct 5, 2014
3. Oct 5, 2014

### Staff: Mentor

Your book is correct. Newton's 2nd law will only give the right answer if expressed with respect to an inertial reference frame. Imagine your cup example. Suppose you select your car as your reference frame while the car is experiencing acceleration or deceleration. As reckoned from this reference frame (i.e., from the inside of the car), if the cup is sliding faster and faster (as a result of the car accelerating), it is doing so without any external force acting on it (neglecting friction between the cup and the dashboard). From the perspective of someone watching these events from the roadside, the cup is still traveling as the same speed that it did before the car started to accelerate. So, as reckoned from the car's frame of reference, Newton's 2nd law gives the incorrect result (no net force, even though the cup appears to be accelerating), while, from the roadside observer's (inertial) frame of reference, Newton's 2nd law gives the correct result (no net force and no acceleration of the cup).

Hope this helps.

Chet