Asolid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 40.0 kg. initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.500 kg, traveling perpendicular to the door at 12.0 m> s just before impact. find the final angular speed

The final angular speed is 0.223 rad/s

Explanation:

By the conservation of angular moment:

ΔL=0

L₁=L₂

L₁ is the initial angular moment

L₂ is the final angular moment

L₁ is given by:

As the door is at rest its angular moment is zero and the angular moment of mud can be considered as a point object, then:

where

r is the distance from the support point to the axis of rotation (the mud hits at the center of the door; r=0.5 m)

v is the speed

m is the mass of the mud

L₂ is given by:

ωf is the final angular speed

The moment of inertia of the door can be considered as a rectangular plate:

M is the mass of the door

W is the width of the door

The moment of inertia of the mud is:

Hence,

with the invention of the automobile, the woman of the house could drive to the store and get groceries. women were also free to socialize more. during world war ii women were allowed to work in factories to the war effort and could drive to work or ride mass transit buses to their jobs.

if they have a finite resultant