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

In summary, a solid door of mass 19 kg and width 128 cm is hit at a right angle by a 0.6 kg mud ball traveling at 16 m/s. The rotational inertia of the door about the hinges is 10.377 kg·m2. The angular velocity of the door after being struck can be calculated using the equation L=mvr and the fraction of initial energy retained by the door-mud ball system is dependent on the value of the angular velocity.
  • #1
mjdiaz89
11
0
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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  • #2
Your equation L=mvr is what you need for part B. This will give you the angular momentum of the projectile.
 
  • #3
huh?
 

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is dependent on the mass and distribution of the object's mass relative to its axis of rotation.

2. How is rotational inertia different from regular inertia?

Regular inertia, also known as linear inertia, is a measure of an object's resistance to changes in its linear motion. Rotational inertia specifically refers to an object's resistance to changes in its rotational motion.

3. How is rotational inertia calculated?

The rotational inertia of an object can be calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. This is also known as the object's moment of inertia.

4. Why is the rotational inertia of the door important?

The rotational inertia of the door is important because it affects how difficult it is to rotate the door around its hinges. A door with a larger rotational inertia will be harder to open and close compared to a door with a smaller rotational inertia.

5. How does the rotational inertia of the door change when the door is opened?

The rotational inertia of the door will change as it is opened because the distance from the axis of rotation to the door's mass will change. As the door moves further away from the hinges, its rotational inertia will increase, making it harder to continue opening the door.

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