Illustration 4.1: Newton's First Law and Reference Frames

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On first glance it may seem like Newton's first law (an object at rest remains at rest and an object in motion remains in motion unless acted on by a net force) is contained within Newton's second law. This is actually not the case. The first law is also a statement regarding reference frames. This is the information NOT contained in the second law. Sometimes the first law is also called the law of inertia. It defines a certain set of reference frames in which the first law holds, and these reference frames are therefore called inertial frames of reference. Put another way, Newton's first law states that if the net force on an object is zero, it is possible to find at least one reference frame in which that object is stationary. There are many frames in which the object is moving with a constant velocity.

A ball popper on a cart (not shown to scale) is shown moving on a track in three different animations (position is given in meters and time is given in seconds). In each animation the ball is ejected straight up by the popper mechanism at t = 1 s. Restart.

Let us first consider Animation 1. In this animation the cart is stationary. But is it really? We know that we cannot tell if we are stationary or moving at a constant velocity (in other words in an inertial reference frame). Recall that if we are moving relative to Earth at a constant velocity we are in an inertial reference frame. So how can we tell if we are moving? How about the cart? We cannot tell if there is motion as long as the relative motion with respect to Earth can be described by a constant velocity. In Animation 1 the cart could be stationary. In this case, we expect—and actually see—that the ball lands back in the popper. However, if the cart was moving relative to Earth and we were moving along with the cart, the motion of the ball and the cart would look exactly the same!

What would the motion of this ball and cart look like if the cart moved relative to our reference frame (or if we moved relative to its reference frame)? Animations 2 and 3 show the motion from different reference frames. What do these animations look like? Both animations resemble projectile motion. The motion of the ball looks like motion in a plane as opposed to motion on a line. Does the ball still land in the popper? Would you expect this? Sure. There is nothing out of the ordinary going on here. Since there are no forces in the x direction, the motion of the ball (and cart) should be described by constant velocity in that direction. Therefore the ball and the cart have the same constant horizontal velocity.

For more on reference frames and relative motion, see Chapter 9.

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