Conceptual question about torque and balls

AI Thread Summary
The discussion revolves around the calculation of torque in relation to a ball rolling on the ground. The original question asks whether torque can be measured from the contact point between the ball and the ground instead of its center. The poster attempts to derive the angular acceleration using this method but encounters incorrect results, specifically obtaining (3/2) instead of the expected (2/3). The conversation highlights the importance of understanding the reference point for torque calculations and the implications of using different pivot points. Ultimately, the poster seeks clarification on their approach and the underlying physics principles involved.
Niles
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[SOLVED] Conceptual question about torque and balls

Homework Statement


Take a look at the following thread:

https://www.physicsforums.com/showthread.php?t=147053

In this thread, the torque is measured from the center of the ball. Can I measure it from the point where the ball and the ground touch each other, so the torque is:

T = mgsin(a)*R = I*alfa?

I tried, and it gives me that a = (3/2)gsin(a), which is wrong - why?
 
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No, then again I get (2/3) rather than (3/2) - but still it doesn't work.
 
Any suggestions? I would really like to know, whether am I wrong or right about this.
 
No suggestions at all :)?
 
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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