Question

(3)(30 pts) Take a picture of a door of the room where you are sitting now and attached it with your solution to this test.

(a) (10 pts) Estimate the mass, width and height of the door, then calculate the moment of inertia of the door with respect to its hinged side (rotational axis) assuming the mass is uniformly distributed over the entire door.

(b) (10 pts) If you apply a constant force of 50 N on the door nub perpendicular to the surface of the door, what is the resulting angular acceleration of your door?

©(10 pts) By how many degrees your door has rotated after 3 seconds?

Answer 1

okay, this problem asks us to estimate numbers

so,

I am taking the following numbers

m = 50 kg

height = 9 meters

width = 4 meters

note that while calculating moment of inertia about the hinge, the height of door does not matter

so,

moment of inertia about hinge is

I = mL² / 3

where L is width of door

I = 50 * 4² / 3

I = 266.66 kg.m²

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Now,

To find the angular acceleration,

= I *

F * L = I *

= F * L / I

= 50 * 4 / 266.66

= 0.75 rad/sec²

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how many degrees it has rotated after 3 seconds

use rotational kinematics

= 1/2 * * t² ( assuming initial angular velocity is zero)

= 1/2 * 0.75 * 3²

= 3.375 radian

or

= 193.4 degree