A student wants to run an experiment to determine how the distribution of mass (location of mass) affects an object`s rotational velocity. For this experiment the student picks 3 rings. One is a wood ring (like a hula-hoop) with all of its mass at the outer edge (A). The next is a ring that has its mass even distributed over the entire right (B). The third ring is a combination of the first two -it has not mass at its center, but the ring is much wider than the first (hula-hoop) ring (C),

Each of the three rings has a different mass and a different diameter.
The students results show that ring A (the hula-hoop) makes it down the ramp the fastest every time and concludes that it must have the highest rotational velocity and the lowest rotational inertia. You know a thing or two about rotational inertia, rotational velocity, and experiments and know that this sounds fishy.
a. What is it about this experiment that might lead the student to draw these incorrect conclusions?
(Describe all things about the experiment that might be flawed)
b. What relationship was the student trying to find?
c. Write a hypothesis for this experiment that addresses the initial question the student tried to investigate.
d. Describe which variable would be the independent variable and why,
e. Describe which variable would be the dependent variable and why.
f. This experiment should have several variables that are kept constant. Name as many constants as possible.

a. There are several flaws in this experiment that may have led the student to draw incorrect conclusions.

First, the student only used three different rings, which may not be representative of all possible distributions of mass. This limited sample size could lead to biased results.

Second, the student did not account for the different masses and diameters of the rings. Mass and diameter can greatly influence the moment of inertia and rotational velocity of an object. Therefore, comparing the three rings without considering these factors may not lead to accurate conclusions.

Third, the student only measured the time it took for each ring to go down a ramp. While this can provide some information about their relative speeds, it does not directly measure rotational velocity or provide a comprehensive understanding of how the distribution of mass affects it. Other factors, such as friction or air resistance, could also influence the results.

b. The student was trying to find the relationship between the distribution of mass (location of mass) in the rings and their resulting rotational velocity.

c. Hypothesis: The hypothesis for this experiment could be: "A ring with mass distributed closer to its center will have a slower rotational velocity compared to a ring with mass concentrated at the outer edge."

d. The independent variable in this experiment would be the distribution of mass (location of mass) in the rings. The student can manipulate this by choosing rings with different mass distributions, such as having all the mass at the outer edge (ring A), evenly distributed mass (ring B), and no mass at the center but a wider ring (ring C).

e. The dependent variable in this experiment would be the rotational velocity of the rings. This can be measured by determining how fast the rings rotate or the time it takes for them to go down the ramp.

f. Several variables should be kept constant in this experiment to ensure valid results. These could include:
- The ramp angle: Keeping the angle of the ramp the same for all trials will ensure consistent conditions for comparing the rotational velocities of the rings.
- The surface of the ramp: Using the same material and surface texture for the ramp will reduce variations in friction and provide consistent conditions for the rings to roll.
- The starting position: Starting each trial from the same height or position on the ramp will eliminate potential variations in initial conditions.
- The shape and size of the rings: Using rings with similar shapes and sizes, other than the variation in mass distribution, will help isolate the effect of mass distribution on rotational velocity.
- Controlling external influences: Minimizing external factors such as air resistance and vibrations during the experiment will help ensure that the measured rotational velocities accurately reflect the effect of mass distribution.