In our hotel there is a revolving door. And I wanted to
consider the different torques each family member could give to the door.

To use this model for problems, lets assume that the door
weighs a total of 100 kg

And lets say each arm of the door is 3m in length.

So if I, standing 1.5 m from the center push on the door
with a force of 50N how much torque do I create?

T=F×r×sinΘ

T= 50N × 1.5m ×
sin (90°)

T=75Nm

Then, lets say my dad, who can push at a force of 60 N, wanted to
match my torque. How far away would he have to be from the center to equal my
torque?

T=F×r×sinΘ

75Nm= 60N × x m × sin
(90°)

x= 1.25 m

And
finally, lets say my mom, who pushes at the same force that I do (50 N), was
pushing in the same direction but at 2 m. what
would be the doors angular acceleration?

ΣT=Iα

Sum of
Torques= T(me) + T(mom)

ΣT=75Nm +
(50N)(2m)

ΣT= 175Nm

Moment of Inertia for
a revolving door= MR

^{2}/3
I= (100kg)(3m)

^{2}/3
I= 300 kgm

^{2}
Then plugging these
into the first equation we can find the angular acceleration (assuming no air
resistance)

ΣT=Iα

175Nm= 300
kg

^{2}m × α
α=0.58
rad/sec

^{2}
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