The moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge is 35.27 kgm².
How to calculate the moment of inertia?
The moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge is calculated using moment of inertia formula for a rectangular plate;
I = ¹/₃ M(L² - d²)
where:
- I is the moment of inertia
- M is the mass of the door
- d is the distance from edge of the door
- L is the height of the height of the door
The given parameters include;
mass, m = 22 kg
height, L = 220 cm
distance, d = 17 cm
The moment of inertia is calculated as follows;
I = ¹/₃ x 22 kg x [ (2.2 m)² - (0.17 m)² ]
I = 35.27 kgm²
The complete question is below:
A 22 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge?