Find moment of inertia for a door

AI Thread Summary
To find the moment of inertia for a uniform, thin solid door rotating on its hinges, the relevant formula is I = 1/3 * m * h^2, where m is the mass and h is the height. For the given door dimensions, the moment of inertia can be calculated using its mass of 23.0 kg and height of 2.20 m. In a separate problem, the time taken for a grinding wheel to reach 1200 rev/min can be determined using torque and angular acceleration equations. The wheel, with a radius of 7.00 cm and mass of 2 kg, accelerates under a constant torque of 0.6000 NxM. Understanding the definitions and equations for moment of inertia and rotational motion is crucial for solving these problems.
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1. A uniform, thin solid door has a height 2.20 m, width 0.870m, and mass of 23.0 kg. Find its moment of inertia for rotation on its hinges. Is any piece of data unneccessary?

2. A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass of 2 Kg. It starts from rest and accelerates uniformly under the action of the constant of torque of 0.6000 NxM that the motor exerts on the wheel.
How long does it take for the wheel to reach its final operating speed of 1200 rev/min ? Through how many revolutions does it turn while accelerating?





Would appreciate any help! Seems easy, but I can't figure it out..like the equation I need to use :confused:
 
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Looks like you need to start with what the definition is for the moment of inertia.
 
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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