Understanding Circular Motion: Is My Combined Proportionality Statement Correct?

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SUMMARY

The discussion centers on the formulation of a combined proportionality statement for circular motion, specifically examining the relationship between centripetal force (F_c), frequency (f), centripetal acceleration (a_c), mass (m), and radius (r). The correct proportionality is established as F_c ∝ f²m/r, confirming that the order of variables is significant. Participants also inquire about the methods used to graphically represent these relationships and measure centripetal acceleration.

PREREQUISITES
  • Understanding of centripetal force (F_c) in circular motion
  • Knowledge of frequency (f) and its units (Hz)
  • Familiarity with centripetal acceleration (a_c) and its calculation
  • Basic principles of proportionality in physics
NEXT STEPS
  • Study the derivation of the centripetal force formula F_c = m * a_c
  • Learn about the relationship between frequency and centripetal acceleration in circular motion
  • Research methods for measuring centripetal acceleration in laboratory settings
  • Explore graphical representations of proportional relationships in physics
USEFUL FOR

Students conducting experiments in physics, educators teaching circular motion concepts, and anyone interested in understanding the dynamics of forces in circular motion.

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doing a lab report on circular motion and was asked to make a combined proportionality statement, just asking yes or no, is this right?

F_c \propto f^{2} \propto a_c \propto \frac{1}{m} \propto r

where "F_c" is the centripetal force,
"f" is frequency in Hz,
"a_c" is the centripetal acceleration,
"m" is the mass in circular motion,
and "r" is the radius of the circumference of motion

is that right? does the order matter?

thanks
 
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What were the graphs that you draw (and found a directly proportional relationship)? How did you measure a_c as a matter of interest?
 
nvrm, the it is F \propto f^2mr

thanks tho
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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