What is the rotational inertia of the door about the hinges?

AI Thread Summary
The discussion revolves around calculating the rotational inertia of a door about its hinges after being struck by a mud ball. The door has a mass of 19 kg and a width of 128 cm, while the mud ball weighs 0.6 kg and hits the door at 16 m/s. The rotational inertia is determined to be 10.377 kg·m² using the formula I = 1/3mr². Participants express confusion regarding the conversion of linear momentum to rotational momentum for calculating the door's angular velocity after impact. The conversation highlights the need to understand angular momentum to solve for the energy retained in the door-mud ball system.
mjdiaz89
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Thank you all for taking the time to help me out. Here's what I'm given:

Homework Statement


A solid door of mass M = 19 kg and width = 128 cm is hit at a right angle by a mud ball of mass m = 0.6 kg, which, as Fig. 10–44 shows, hits the door at the edge with speed v = 16 m/s and sticks.


Figure 10-44

(a) What is the rotational inertia of the door about the hinges?
10.377 kg·m2
(b) What is the angular velocity of the door after having been struck?
________ rad/s
(c) What fraction of the initial energy does the moving door–mud ball system retain?
_______


Homework Equations


p=mv
I= 1/3mr^2
L=mvr


The Attempt at a Solution


-Part A was simply 1/3mr^2
-Part B confuses me because I have to somehow make a linear momentum into a rotational momentum, while not forgetting the moments of inertia. Someone please shed some insight to this simple problem.
-Part C = I need part B :/
 
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Your equation L=mvr is what you need for part B. This will give you the angular momentum of the projectile.
 
huh?
 
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