As a subway car leaves the platform, the passengers are advised to hold on. From their point of view, it seems that there is a sudden force that pushes them to the back of the car. Physicists prefer to think of this situation from the point of view of someone standing on the platform: the car has suddenly started moving forwards, and due to inertia the people inside tend to stay where they are.

While the subway car is moving along the tracks, the passengers don't notice the motion, so long as it has constant speed and direction. However, where the track curves, the train changes direction, while the passengers continue in a straight line (if they don't hold on!); from their point of view, it seems that a force has thrown them outwards. Here again, the physicist prefers to discuss this from a fixed point of view: the "outwards" motion is actually a straight-line continuation of the previous motion and there is no outwards force.

A bubble level works the same way as the subway car (using either description), with the liquid inside taking the role of the passengers, and the bubble inside making the liquid's motion visible. While at rest or moving with constant speed on a level surface, the bubble is centered; but as the velocity of the level increases, the liquid "gets left behind." Likewise, as the velocity decreases, the liquid tries to keep going forward making the bubble shift backwards, in the direction of the deceleration. In both cases, either positive or negative acceleration, the bubble moves to one edge of the level, and points in the direction of the acceleration. When the velocity has constant direction, so that only the speed changes, the acceleration is in the same (or opposite) direction; but changing direction of motion also involves acceleration. We hope that when you moved the level in a circle, you observed that the bubble tended to point towards the center: this is the direction of the acceleration when the speed is constant.

Calculating acceleration is straight forward when motion is in just one direction (so that all that is changing is the speed). When the velocities are in different directions we have to learn how to do the arithmetic of numbers that have directions attached to them; for the purposes of this course we will only use a qualitative definition of acceleration: if a moving object veers to the right, it has accelerated to the right, whether its speed has changed or not. Note that this agrees with the claim that a level moving in a circle is accelerating towards the center of the circle.

Check the box when you are done:   

Discussion of the unit on acceleration