How do you calculate tension and moment of inertia from given information?

AI Thread Summary
To calculate the tension in the rope, the correct approach involves using the formula T = m(g sin θ - a), where g is the acceleration due to gravity. For the moment of inertia, the torque can be found using τ = r * T, and then applying the relationship τ = I * α, where α is the angular acceleration. The angular acceleration can be derived from the linear acceleration using α = a/r. By rearranging these equations, the moment of inertia I can be calculated as I = τ/α. Understanding these principles is crucial for solving problems involving tension and moment of inertia in dynamics.
mspaic
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Hey
I am doing some reading on inertia and stuff and am having problems with these questions:

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An m = 11.9 kg mass is attached to a cord that is wrapped around a wheel of radius r = 12.3 cm

The acceleration of the mass down the frictionless incline is measured to be a = 1.91 m/s2. Assuming the axle of the wheel to be frictionless, and the angle to be θ = 33.1°
a)determine the tension in the rope.
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b)Determine the moment of inertia of the wheel.
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ok for a i did :
T=cos angle *m*a but that doesn't give me the right answer..
 
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ok i got a
i gues they wanted torque
 
anyone know how to calcluate the moment of inertia from the information given
 
Last edited:
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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