How Does Angular Acceleration Affect Rotational Motion?

[rockmorg]

Hey all, thought I should ask about a couple problems...

1 - A rotating door is made from four rectangular glass panes, as shown in the drawing. The mass of each pane is 95 kg. A person pushes on the outer edge of one pane with a force of F = 80 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration.

This says it is about a fixed axis so I don't know how that changes it, but it doesn't seem like I have enough information for one of the rotational kinematics equations...

2 -

A thin uniform rod is initially positioned in the vertical direction, with its lower end attached to a frictionless axis that is mounted on the floor. The rod has a length of 1.90 m and is allowed to fall, starting from rest. Find the tangential speed of the free end of the rod, just before the rod hits the floor after rotating through 90°.

This one seems like it should be really easy, but I'm not sure. I'll need the time it takes for the rod to fall, and I assume that I could use moment of inertia somehow because they specifically say thin uniform rod? Then convert the angle it fell thru to radians...?

Thanks much, any help is appreciated!
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rockmorg

 

[Nm]

For problem 1, first find the rotational inertia of the door (includes all 4 panes). Then, you can use the torque formula to find the angular acceleration. Remember the force is perpendicular to the pane.

 

[quicknote]

Hello rockmorg,

Thank you for asking about these rotational motion problems. Let's take a look at each one individually:

1. For the first problem, you are correct in noting that the fact that it is a fixed axis changes the situation. In this case, we can use the equation τ = Iα, where τ is the torque applied, I is the moment of inertia, and α is the angular acceleration. We can find the moment of inertia of the door by treating it as a system of point masses and using the parallel axis theorem. Once we have the moment of inertia, we can solve for α using the given force and the equation τ = Iα.

2. As for the second problem, you are on the right track in thinking about using the moment of inertia and converting the angle to radians. One approach you could take is to use the equation τ = Iα again, but this time solving for the angular acceleration. Then, you can use the kinematic equation ωf = ωi + αt to find the final angular velocity. From there, you can use the relation v = rω to find the tangential speed of the free end of the rod.

I hope this helps! Remember to always carefully consider the given information and use the appropriate equations for rotational motion. Best of luck with your studies.