Calculating Forces, Moments, and Angular Speed in a Rotational System

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The discussion focuses on calculating forces, moments, and angular speed in a rotational system involving a 12 kg mass on a 37-degree incline and a wheel with a 10 cm radius. Participants emphasize the need for a free body diagram (FBD) to visualize the forces acting on the mass and the wheel. Key calculations include determining the force in the rope, the moment of inertia of the wheel, and the angular speed after 2 seconds of rotation. Clarifications about the setup, such as whether the mass is sliding down the incline and the relationship between the mass and the wheel, are also sought. The conversation highlights the importance of understanding the dynamics of the system to solve the problem effectively.
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Can someone help me set this up? Please?

A 12 kg mass is attached to a cord that is wrapped around a wheel with a radius of 10 cm. The acceleration of the mass down the frictionless incline is measured to be 2 m/s^2. Assuming the axle of the wheel to be frictionless, determine: a) the force in the rope, b) the moment of inertia of the wheel, and c) the angular speed of the wheel 2 s after it begins rotating, starting from rest.

I'll take any help that I can get, and I really appreciate anyone helping me out. Thank you.
 
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I'm pretty sure you might need the slope of the incline for this problem.
 
I forgot to add that in the problem. There is a 37 degree incline.
 
Do you have a picture? Is the mass sliding down the incline? Is the wheel the 12 kg mass?
 
Rebel,

Where are you having problems? Can you draw a FBD?
 
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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