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Group 1: The points/concepts have been captured very well.

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If experimental measurements contain uncertainties, how can laws be developed based on experimental
evidence?

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Group 2: Good writing! You have understood the concepts very well. Well written!

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How does graphical analysis allow for the determination of other physical quantities?

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How effectively do the equations of motion model Newton’s laws of dynamics?

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Experimental uncertainties are the range of errors that may persist in experimental data. There are a number of experimental uncertainties, such as random error, systematic error, parallax error, etc. However, accurate information can be deduced from results with uncertainties in several ways, which allow us to develop laws based on experimental evidence. Some of these ways include:

1) Ensuring reliability: Reliability is one of the key factors that is affected by the uncertainties in measurements. One of the ways to ensure reliability is by repeating the experiment several times and deducing an average value. Not only does this give us more reliable data, it also potentially allows us to achieve more accurate data as anomalies appear while repeating experiments which can be discarded for more accurate results. Another way to ensure reliability is drawing a graph with a set of data values and observing the graph, such as its gradient and shape.

2) Adjusting experimental data: Sometimes uncertainties occur due to systematic error. This is when an error occurs due to a problem in one of the apparatuses, so that each reading is off from the true value by the same amount. So, scientists adjust their data based on the systematic errors they know of so that the level of uncertainty in their measurements is minimized. For example, if there is zero error in a stopwatch of 0.1 seconds, the scientist would deduct 0.1 seconds from each value that they get from the stopwatch. This helps eradicate the uncertainty.

3) Ensuring accuracy: Whenever possible, scientists try to ensure the highest level of accuracy in their experiments. Accuracy is how close the experimental value goes to the true value. From the degree of incline of a ramp to the amount of water in a beaker, scientists try to use exact and accurate measurements so as to reduce the chances of uncertainties occurring. Furthermore, if scientists know the true value of the data they are collecting, they can adjust and repeat their experiments based on how accurate their acquired data is, rendering uncertainties even more unlikely to occur.

While uncertainties will always persist in any experiment, minimizing their significance and their frequency can help acquire nearly if not true values of data in experiments. This helps ensure that data is reliable and accurate, and thus helps us build laws upon experimental evidence.

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In rotational motion, angular displacement (θ) is analogous to linear displacement (s) in linear motion. Just as an object can move a certain distance along a straight path, an object in rotational motion can rotate through a certain angle. Thus we can find the  relationship where we can see that the linear displacement deals with the regular SI units and it travels in a linear way. However in angular displacement, the angle which the circular motion relates to is the key variable, thus it shows the relation that the variable is influencing the linear and rotational motion of the object. Just how an object can move in a straight linear path, it can move in a rotation over a certain angle.

Angular velocity (ω) is the rate of change of angular displacement (θ) with respect to time (t). Linear velocity (v) is the rate of change of linear displacement (s) with respect to time (t). The relationship between angular velocity and linear velocity is given by: v = rω, where "r" is the radius from the axis of rotation to the point of interest.

Thus we can see how rotational motion equations are heavily influenced by the equations of linear motion, as the only difference is that the key variable changes depending on the type of motion. The displacement concept is infused with a circle, more specifically 2pi, as that's the entire angular maximum of a circle. Thus we understand that the displacement can be deduced using that. So we can say that the rotational motions are influenced by the linear equations due to their close connection, and having similar supporting variables such as time.

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Group 3: Excellent responses. Very conceptual responses. Well done!

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Group 4: Good writing! You have understood the concepts very well. Well written!

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How are the equations for rotational motion related to those for linear motion?

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Graphic analysis is a very essential tool in science which allows the determination of multiple physical quantities just by simply studying it. Physical quantities may be derived from graphs in many ways, such as:
- The gradient of a graph: The graph's line itself can be used to derive many different physical quantities, such as the gradient of a speed-time graph can be used to derive acceleration.
- Areas under the curve: On a graph, the area under a curve can represent physical quantities. Such as, the area under the gradient of a speed-time graph can be used to determine the distance covered.
- The slope of a curve: From a curve, we can also derive much information about something. For example, a linear curve on a speed-time graph can show us how an object is uniformly accelerating.
- Interceptions of axis in a graph: A graph's axes-intersection points might provide information. For instance, the startling position of an object in motion is represented by the y-intercept in a graph of displacement vs time, whereas the starting or stopping time of the object is shown by the x-intercept.
Curvature: A graph's curvature at a particular location can reveal details about a quantity's pace of change. For instance, the curvature of a location vs time graph may be used to determine an object's acceleration.

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1. First Law (Law of Inertia): An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This is reflected in the equation v = u + at, where if a (acceleration) is zero, the velocity (v) remains constant (u).

2. Second Law (F = ma): Newton's second law states that the force acting on an object is equal to the mass of the object times its acceleration (F = ma). This law is directly reflected in equations of motion, as it quantitatively relates force, mass, and acceleration. Using these equations, you can calculate the motion of an object when forces are applied.

3. Third Law (Action-Reaction): Newton's third law states that for every action, there is an equal and opposite reaction. While equations of motion do not directly represent this law, they are consistent with it. When you apply forces to objects, the equations of motion predict how the object will respond to these forces, including any equal and opposite reactions.

However, it's important to note that these equations have limitations. They assume a constant acceleration, and they don't apply when forces are changing or when dealing with very high speeds (where relativity becomes important) or very small particles (where quantum effects are significant).