How Do You Calculate the Rotational Inertia of a Rotating Door?

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SUMMARY

The discussion focuses on calculating the rotational inertia of a rotating door composed of four rectangular glass panes, each weighing 76 kg. The torque applied to the door is calculated as 66 Nm using the formula torque = distance × force, where the distance is 1.2 m and the force is 55 N. The user suggests using the formula I = 1/3ML² for each pane, multiplied by four, to determine the total rotational inertia. The conversation also touches on the relationship between torque, rotational inertia, and angular acceleration, which is crucial for solving related problems.

PREREQUISITES
  • Understanding of rotational dynamics and inertia
  • Familiarity with torque calculations
  • Knowledge of angular acceleration concepts
  • Basic physics principles related to force and motion
NEXT STEPS
  • Study the derivation and application of the rotational inertia formula I = 1/3ML²
  • Learn how to calculate angular acceleration using the formula α = τ/I
  • Explore the concept of torque in rotational systems and its relation to force
  • Practice problems involving the motion of rigid bodies, particularly in rotational dynamics
USEFUL FOR

Students preparing for physics exams, particularly those focusing on rotational dynamics, as well as educators teaching concepts related to torque and rotational inertia.

Nm
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A rotating door is made from four rectangular glass panes, as shown in the drawing. The mass of each pane is 76 kg. A person pushes on the outer edge of one pane with a force of F = 55 N that is directed perpendicular to the pane.
09_34.gif

a.) Find the rotational inertia of the door.
b.) Find the magnitude of the door's angular acceleration.
c.) Find the time it would take to rotate the door a half-circle (assuming it started from rest.)
I have tried calculating the torque for the pane to be (1.2m)(55N) = 66 Nm. I think the rotational inertia should be I = 1/3ML^2 multiplied by 4 for each pane since it is spinning away from the center of mass (edge). Can someone tell me if this is correct? I don't know how to continue this problem...Thanks.
 

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I figured out the solutions so never mind.
 
Nm said:
A rotating door is made from four rectangular glass panes, as shown in the drawing. The mass of each pane is 76 kg. A person pushes on the outer edge of one pane with a force of F = 55 N that is directed perpendicular to the pane.
09_34.gif

a.) Find the rotational inertia of the door.
b.) Find the magnitude of the door's angular acceleration.
c.) Find the time it would take to rotate the door a half-circle (assuming it started from rest.)
I have tried calculating the torque for the pane to be (1.2m)(55N) = 66 Nm. I think the rotational inertia should be I = 1/3ML^2 multiplied by 4 for each pane since it is spinning away from the center of mass (edge). Can someone tell me if this is correct? I don't know how to continue this problem...Thanks.



I thought torque was rotational inertia multiplied by acceleration(in radians). You found your torque by multiplying the distance by the force? Can you exlplain your steps bcz I have a test on Friday on Rotation, and this could be very useful
 

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