Forces & Motion

Linear motion

Dynamics is a very interesting topic in physics, we can find it everywhere in our daily life. Many students tend to skip this topic, just because they really cannot grab the main idea of this topic. In this section, we will discuss about some important terms in dynamics and the characteristic. Before we start to learn more about dynamics, student should be clear about the meaning of the terms we usually use, so that you will not confuse when we go further in this topic.

Scalar and vector quantity

• Scalar quantity – has magnitude but no direction
• Vector quantity – have magnitude and direction

In dynamics, the direction of motion is incredibly important!!! Some students will make mistake about the “+” and “-” sign, when they substitute the value in an equation. “+” and “−” signs have no physical meaning in mathematic. In physics, we give them a new definition, “+” indicate the positive direction “–” indicate the negative direction.

Figure 2

Figure 2.0 shows x and y axes. Usually we set right and upward direction as a positive direction, left and downward direction as negative direction. Start from now you must remember them until you finish your SPM!! The direction is extremely important!!

Distance and displacement

Distance – the total length travels by the object. (Scalar quantity)

Displacement – the shortest distance between object and origin. (Vector quantity)

Figure 2.1

Figure 2.1 shows a circle with radius 7m, from the formula; we know that the circumference is 44m. A and B located at the same point. If an object move along the circumference from A to B,

• the distance in this travel is 44m
• the displacement in this travel 0m.

Since the A and B locate at same point, the shortest distance between object and origin is zero.

Figure 2.2 Pythagorean theorem

If a person move from point A to B then to C,

• the distance in this travel is 7m
• the displacement in this travel 5m.

Since the displacement is the shortest distance between object and origin that we can calculate the shortest distance which is CA by using Pythagorean theorem.

Figure 2.3

If a person moves from A to B then back to A and go to C. The total distance travel by the person is 5m, but the displacement is -1m. Since A is set as the origin, when the person moves from A toB, which can be said as the person moves in positive direction. When the person turns back fromB to C, it is in the negative direction. Hence, students have to add the minus sign.

Displacement = 2m + (-2m) + (-1m) = -1m

“Please take note that not 2m – 2m – 1m but it should be 2m + (-2m) + (-1m), the reason for me to use + (- 2m) is that, in my view, there is no minus in dynamics; instead I will sum up everything. If it is in negative direction I will add a minus sign in front of the numeric value to indicate its direction.” 

Speed and velocity

In our daily life, we may say “Ei, that car move very fast leh.”, but how fast is the car? In physics, the term “speed” and “velocity” is to describe the degree of quickness of a moving object. These terms are very important to traffic police officers, without the concept of speed, they cannot catch offenders who speed. In our daily life, most of us would usually emphases on speed and yet the direction is not important. As long as people know how fast the car move, then we are happy. But it may not be true in physics world, we are more concern on the velocity, because the direction of the object is very important when we want to calculate its velocity.

• Speed can be defined as the rate of change of distance. It is a scalar quantity, since it is closely relate to distance.
• Speed = distance / time
• Velocity defined as rate of change of displacement. It is vector quantity.
• Velocity = displacement / time

Rate of change of displacement tell you on the displacement change with respect to time. For example, if an object move with velocity of 2ms^-1 and start from the rest. When t=0, d=0; t=1, d=2; t=2, d=4.

Figure 2.4

Figure 2.4 shows the graph of displacement against time. From the graph, we know that the gradient of the graph is d/t and it is exactly the velocity. Hence we can make a conclusion that the gradient of the graph of displacement against time is equal to velocity. This is a very important concept, but student seldom take note about it. In this graph, the gradient is constant (velocity constant), and is equal to 2ms^-1

Another important thing is that the direction is very important to velocity. When we mention about constant velocity, it means that the object travels with constant magnitude and in same direction. When the direction change, although the magnitude still the same, we cannot say it have a constant velocity.

Figure 2.5

Figure 2.5 shows a person move with 2ms^-1 along a circular path. The magnitude of the quickness is the same, but the direction keeps changing. Hence we say that the velocity of this person keep changing when he moves through the path.

Acceleration

• Acceleration defined as the rate of change of velocity
• Acceleration = velocity / time

Therefore what we can say it that is in the graph of velocity against time, the gradient of the graph should be the acceleration.

In figure below, it show the graph of velocity against time for the motion in the previous meat (Figure 2.5 )  Notes – Force and Motion (Part 4).

Figure 2.6

The gradient of the graph is zero, therefore the magnitude of acceleration = 0 m . But!! Since the direction of that person keeps changing, the velocity keeps changing. Then the person experiences acceleration, just because the acceleration defines as the rate of change of velocity. The acceleration appears here is the centripetal acceleration. We always experience it when our car makes a sudden turn.

Some tips about the graph.

In dynamics, we usually deal with the area under the graph and the gradient of the graph. How we determine the gradient of a curve? Since some graph of motion present in the curve shape.

The gradient of a point in a curve can be determined by draw a straight line at that point (tangent) and calculate the gradient of that line. We call it the instantaneous velocity or instantaneous acceleration in corresponding graph.

In the graph above, we can obtain the gradient m1 and m2 by draw the line on corresponding point. By looking on the steepness of the line, easily we know that the m1 is larger than m2. Since the line for m1 is steeper than the line for m2. From this information we can conclude that the gradient of this graph decrease.

Graph of displacement versus time.

In previous section, we learned v = s/t. In the graph of s versus t, the gradient of the graph equal to s/t. Therefore what we can conclude is that the gradient of the graph s versus t is equal to the velocity.

In the graph above shows a linear graph, the gradient is a fixed value. From graph, obviously the object has a constant velocity.

In the graph above shows a curve, the steepness of the curve reduce. Hence we deduce that the velocity of the object decrease since the gradient decrease.

The steepness of the curve in the graph above increases, therefore the velocity keep increases as the time pass through.