Calculating Position of CM & Moment of Inertia for Weighted Wheel

AI Thread Summary
The discussion revolves around calculating the center of mass (CM) and moment of inertia for a weighted wheel. The CM was determined to be 3.125 cm from the center of the wheel. Participants discussed the application of the parallel axis theorem to calculate the moment of inertia, emphasizing the need to find the moment of inertia for both the wheel and the weight separately before combining them. There is a shared sentiment about the lack of thorough instruction on important physics concepts like the parallel axis theorem in their class. Overall, the conversation highlights the challenges faced in applying theoretical concepts to practical problems in physics.
Stryder_SW
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Homework Statement


A thin 7.0 kg wheel of radius 32 cm is weighted to one side by a 1.0 kg weight, small in size, placed 25 cm from the center of the wheel.

(a) Calculate the position of the center of mass of the weighted wheel.
*edit* found the CM, its 3.125cm from the center *edit*
(b) Calculate the moment of inertia about an axis through its CM, perpendicular to its face.
*edit*SOLVED*edit*

2. The attempt at a solution
*edit*I realize I need to use the parallel axis theorem on part b, but I don't really understand how to apply it.*edit*
 
Last edited:
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Hi Stryder_SW! :smile:
Stryder_SW said:
(b) Calculate the moment of inertia about an axis through its CM, perpendicular to its face.
…
a nudge in the right direction would be greatly appreciated.

nudge nudge …

from the PF Library … Parallel axis theorem: the moment of inertia of a body about an axis is IC + md2

where m is the mass, d is the distance from that axis to the centre of mass, and IC is the Moment of Inertia about the parallel axis through the centre of mass.

:wink: :wink:​
 
Has your class talked about the parallel axis theorem? You have here two bodies, and it is not difficult to find the MMOI for each of them separately with respect to their own CM. Now you need to transfer that MMOI to their common CM and add them.
 
No, unfortunately my class fails at teaching physics. We tend to skip over these important theorems that make our lives so much easier.
 
I realize I need to use the parallel axis theorem, but I'm having a hard time applying it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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