A professor\'s office door is 0.91 m wide, 2.0 mhigh, 4.2 cm thick; has a mass o

Question

A professor's office door is 0.91 m wide, 2.0 mhigh, 4.2 cm thick; has a mass of 21 kg , and pivots on frictionless hinges. A "door closer" is attached to door and the top of the door frame. When the door is open and at rest, the door closer exerts a torque of 5.6 Nm .

Part A

What is the moment of inertia of the door?

Express your answer using two significant figures.

Part B

If you let go of the open door, what is its angular acceleration immediately afterward?

Express your answer using two significant figures.

Explanation / Answer

a)

Moment of inertia about edge axis I = 1/3.Mr^2

M = 21 kg

r = 0.91 m

I = (1/3)(21kg)(0.91)^2 = 5.7967 kg.m^2

b)

Ang.accel.

d/dt = torque / mom. of inertia

d/dt = 5.6 / 5.7967

d/dt = 0.9660 rad/s^2

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