The student is expected to generate and interpret graphs and charts describing different types of motion, including the use of real-time technology such as motion detectors or photogates AND identify and describe motion relative to different frames of reference.
Real-time technology, such as photogates and motion detectors, can be used to measure motion and generate graphs. Graphs can be used to show how an object moves.
Different aspects of an object’s motion, including the object’s past or future position or speed, can be determined using charts and graphs.
A closed system is two or more objects isolated from external forces. The choice of where the system is being viewed is called the frame of reference.
If a system is moving with a constant velocity, the laws of mechanics apply to all the objects whether viewed from inside or outside of the system.
Two systems moving with a constant velocity can be viewed from either system, with the laws of mechanics being the same in either system.
If a system is accelerating, motion will be measured differently in the two different frames of reference, from inside and outside the system.
Position and Time Graphs
The motion of an object can be interpreted in many different ways. Graphs can be used to show how an object moves. Different types of motion, including an objects past or future position or speed, can be determined and expressed using charts and graphs. The motion of an object can have either a positive or negative value showing the direction of the motion. Position-time graphs are useful in visualizing an objects motion relative to a starting point. The x-axis (vertical axis) is labeled with time and the y-axis (horizontal axis) labeled with position. On the graph, the starting point of the object is the reference point at time = 0. As time passes, the line of the graph moves away from the y-axis to the right. If the object never moves, then the line of its motion will just be a horizontal line parallel to the x-axis. If the object does move away from its starting point, then the line of the graph shows this by moving up or down along the y-axis.
Slope Indicates Motion
The slope of the line describes the speed of the object. If the slope is constant, the speed is constant. If the slope is zero, the object is not moving. If the slope is changing, the speed is changing. Faster objects have steeper slopes and slower objects have flatter slopes. A lines slope indicates an objects motion.
The s-t graph below shows the status of motion for an object.
Besides using a graph, the object’s motion can be also expressed utilizing the chart below. When the students are collecting data, it is easier for them to first collect the information in the form of a chart and then transfer the information into a graph. In creating a chart, it is important to define an origin and to measure every position recorded relative to this origin point. The position should include a measurement of magnitude, or distance from the origin, and a direction, the direction in which the motion occurred relative to the origin. A constant speed moving closer to the origin appears differently on the graph than the same speed moving away from the origin.
Relative Motion Affected by Frame of Reference
Motion is a relative concept, since it depends on how you look at it. The choice of where the system is being viewed is called the frame of reference. A closed system is two or more objects isolated from external forces, and it is a part of the universe that is isolated from outside. It does not allow any exchange of external matter or energy.
Inertial Frame of Reference
An inertial frame of reference has a constant velocity. That is, it is moving at a constant speed in a straight line, or it is standing still. Understand that when something is standing still, it has a constant velocity. Its velocity is constantly zero meters per second. To say that the velocity of a frame of reference is constant is the same as saying that the frame is not accelerating. So, we could define an inertial frame of reference to be a coordinate system which is not accelerating.
Such a constant velocity frame of reference is called an inertial frame because the law of inertia holds it in. That is, an object whose position is judged from this frame will tend to resist changes in its velocity; it obeys the law of inertia. An object viewed with this frame will not spontaneously change its velocity. An object within this frame will only change its velocity if an actual non-zero net force is applied to it.
There are several ways to describe an inertial frame:
An inertial frame of reference is a frame of reference with constant velocity.
An inertial frame of reference is a non-accelerating frame of reference.
An inertial frame of reference is a frame of reference in which the law of inertia holds.
An inertial frame of reference is a frame of reference in which Newton’s laws of motion hold.
In an inertial frame of reference no fictitious forces arise.
For example juggling a set of balls while stationary on a bus. The juggler on the bus could not determine that the bus was moving based on any clues gathered from the motion of the balls. They would move through the air within the moving bus exactly as if they were being tossed about within a still room - as long as the bus traveled smoothly down a straight road at constant speed; that is, as long as the bus moved with a constant velocity. The laws of physics of typical mechanics are always the same when it is done within a constant velocity frame of reference.
Constant Velocity Systems
In World War II, a pilot flying a plane spotted a tiny object outside the left side of the cockpit, which did not appear to be moving, he reached out and caught it with his hand and found out it was a bullet!
Two systems moving with a constant velocity can be viewed from either system, with the laws of mechanics being the same in either system. The pilot and the bullet were moving at the same constant velocity, and therefore the relative velocity between the two systems is zero. From the viewpoint of the pilot, the bullet was at rest, motionless.
In addition, if a system is moving with a constant velocity, the laws of mechanics apply to all the objects whether viewed inside the frame of reference or from outside the frame of reference. Lets go back to the pilot story. If the plane were traveling at a constant velocity, the laws of mechanics can be applied to the chairs, the pilots helmet, the front window glass and all the other objects on the plane.
Non-Inertial Frames of Reference
The example of the juggler on the bus would cease to be an inertial frame of reference while it changed its velocity. That would happen if it slowed down, or if it sped up, or if it turned around a corner. Each of these changes in velocity would constitute an acceleration. And, while the bus was accelerating, the act of juggling could get quite difficult. For example, if the bus driver slammed on the brakes while some of the balls were in flight, those balls would seem to fly forward from the juggler’s perspective, assuming that the juggler was facing the front of the bus. From the viewpoint of the juggler it would seem as if some unknown force had pushed the balls away from them, making them fly up toward the front of the bus. The juggler, too, would feel a push toward the front of the bus. But remember, in this situation the bus is no longer an inertial frame of reference; its velocity is changing; it is now an accelerating frame of reference. So, the law of inertia and Newton’s laws of motion no longer hold. This accelerating frame is called a non-inertial frame of reference.
However, if a system is accelerating, motion will be measured differently in the two different frames of reference. For instance, we have
In the first system, the velocity is zero. Thus, we can observe that the second system is accelerating with an acceleration, a. Moreover, all the objects in the second system have the same acceleration.
But if we stand inside the second system, which is a different frame of reference, all the objects are at rest. They do not have the acceleration. This example tells us that the choice of a frame of reference is vitally essential.
A non-inertial frame of reference does not have a constant velocity. It is accelerating. There are several ways to imagine this motion:
The frame could be traveling in a straight line, but be speeding up or slowing down.
The frame could be traveling along a curved path at a steady speed.
The frame could be traveling along a curved path and also speeding up or slowing down.
Such an accelerating frame of reference is called a non-inertial frame because the law of inertia does not hold in it. That is, an object whose position is judged from this frame will seem to spontaneously change its velocity with no apparent non-zero net force acting upon it. This completely violates the law of inertia and Newton’s laws of motion, since these laws claim that the only way an object can change its velocity is if an actual non-zero net force is applied to the object. Objects just do not start to move about here and there all on their own.