How to Graph Moment of Inertia and Frictional Torque?

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SUMMARY

The discussion focuses on graphing the moment of inertia (I) and frictional torque of a bicycle wheel using the equation rm(g-a) = I(a/r) + Frictional Torque. The variables m (mass) and a (acceleration) are identified as the x and y variables for the linear graph, with I representing the slope and Frictional Torque as the y-intercept. Constants such as r (radius) and g (acceleration due to gravity) also play a role in determining the slope and intercept values. The goal is to manipulate the equation to facilitate a linear representation for analysis.

PREREQUISITES
  • Understanding of linear equations (y = mx + b)
  • Knowledge of moment of inertia and frictional torque concepts
  • Familiarity with basic physics principles related to rotational motion
  • Ability to manipulate algebraic equations for graphing purposes
NEXT STEPS
  • Learn how to derive linear equations from physical formulas
  • Explore graphing techniques for rotational dynamics
  • Study the relationship between moment of inertia and angular acceleration
  • Investigate methods for calculating frictional torque in mechanical systems
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in analyzing rotational motion and torque in mechanical systems will benefit from this discussion.

cam borrett
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Homework Statement



The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation:
rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants corresponding to the slope and intercept of the proposed linear graph.

r = 0.018m
m=0.200kg
g=9.8m/s^2
a=0.002812
I=?
Frictional Torque= ?

Homework Equations



(1) rm(g-a) = I(a/r)+Frictional Torque.

(2) y=mx+b

3. The Attempt at a Solution

Im not sure if I am 100% right on this but, equation one could take the form of equation two.
m being I.
x being what's changing, ie. acceleration
b being the y intercept, ie frictional torque

Just unsure where to go from there a how to graph it.
 
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cam borrett said:
rm(g-a) = I(a/r)+Frictional Torque.
Presumably these variable relate to a physical set-up of some kind. Please describe it.
 
The two variables are m and a. Try and rewrite the equation so that they become the x and y variables in the linear equation (or a combination of the variables!). The frictional torque and moment of inertia should then part of gradient and y-intercept values (r and g will also appear in these).
 
Last edited:
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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