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

Click For Summary
SUMMARY

The rotational inertia of a solid door about its hinges, given a mass of 19 kg and a width of 128 cm, is calculated to be 10.377 kg·m². The door is struck by a mud ball of mass 0.6 kg traveling at 16 m/s, which sticks upon impact. The discussion highlights the use of the equation I = 1/3mr² for calculating rotational inertia. Additionally, the conversion of linear momentum to angular momentum is necessary for determining the angular velocity of the door post-impact.

PREREQUISITES
  • Understanding of rotational inertia and the formula I = 1/3mr²
  • Knowledge of linear momentum and its relation to angular momentum
  • Familiarity with the concepts of mass, velocity, and energy conservation
  • Basic physics equations involving momentum (p = mv) and angular momentum (L = mvr)
NEXT STEPS
  • Learn about angular velocity calculations in rotational dynamics
  • Study the conservation of angular momentum in collision scenarios
  • Explore energy retention in inelastic collisions
  • Investigate the effects of different mass distributions on rotational inertia
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of rotational dynamics and momentum conservation in collision problems.

mjdiaz89
Messages
10
Reaction score
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 :/
 
Physics news on Phys.org
Your equation L=mvr is what you need for part B. This will give you the angular momentum of the projectile.
 
huh?
 

Similar threads

Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
6
Views
5K
Replies
5
Views
1K
  • · Replies 3 ·
Replies
3
Views
13K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K