Equation for torque of a cylinder, a hollow cylinder, and a sphere.

AI Thread Summary
The discussion focuses on finding the equations for torque related to a solid cylinder, hollow cylinder, and sphere rolling down an incline. Torque is defined as the rate of change of angular momentum, with the relationship T = Iα, where T is torque, I is the moment of inertia, and α is angular acceleration. The user expresses confusion about how to start solving the problem and seeks clarification on the equations involved. Understanding the moment of inertia for each shape is crucial for calculating torque. The conversation emphasizes the importance of grasping these fundamental physics concepts.
nlingraham
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Homework Statement



What is the equation for the torque of a cylinder, a hollow cylinder, and a sphere rolling down an incline?

Homework Equations



This is what I don't know

The Attempt at a Solution



I have no idea where to start.
 
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Torque is the rate of change of angular momentum

if angular momentum = Iω, that is torque then?
 
What is the equation for torque? Similarly to F = ma, the equation for torque is
T = I\alpha
 
Thanks, you guys are awesome
 
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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