How Does a Bullet Impact Affect the Angular Velocity of a Door?

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In summary: The bullet has linear momentum before impact, which is converted into angular momentum after impact. The key to solving this problem is to find the angular momentum of the bullet before impact and set it equal to the angular momentum of the door after impact. Then solve for the angular velocity of the door. In summary, to find the angular velocity of a door after a 10 g bullet embeds itself in the door, use conservation of angular momentum by setting the angular momentum of the bullet before impact equal to the angular momentum of the door after impact. This can be calculated using the formula w = (3mv) / (ML^2), where w is the angular velocity, m is the mass of the bullet, v is its velocity, M is
  • #1
sp3sp2sp
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Homework Statement



A 10 g bullet traveling at 370 m/s strikes a 8.0 kg , 0.80-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open.
What is the angular velocity of the door just after impact?
Express your answer to two significant figures and include the appropriate units.

Homework Equations


use conservation of momentum for slab about edge: linear momentum = angular momentum
mv = Iw
I = (1/3)ML^2 (for a slab)
w = (3mv) / (ML^2)
(w = omega)

3. The Attempt at a Solution
w = (3mv) / (ML^2)

w = (3* 0.01kg * 370m/s) / (8.0kg * 0.80kg^2)
w = 2.167 = 2.2 rad/s
= wrong

cant see what I am doing wrong, thanks for any help
 
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  • #2
sp3sp2sp said:
use conservation of momentum for slab about edge: linear momentum = angular momentum
o_O

Linear momentum and angular momentum are different quantities with different units. They cannot be set equal. In this case, only one of those is conserved.

Hint: Use conservation of angular momentum. (What's the angular momentum of the bullet just before impact?)
 
  • #3
bullet doesn't have any angular momentum before impact So Iw = 0?
 
  • #4
sp3sp2sp said:
bullet doesn't have any angular momentum before impact
Sure it does (about the door hinge axis). Read this: Angular Momentum of a Particle

sp3sp2sp said:
So Iw = 0?
No.
 

FAQ: How Does a Bullet Impact Affect the Angular Velocity of a Door?

1. How does a bullet hitting a door affect the door's structural integrity?

When a bullet hits a door, it creates a small hole in the door's surface. Depending on the type of door and the caliber of the bullet, the hole may be larger or smaller. However, in most cases, the structural integrity of the door is not significantly affected. The door may still be able to function properly and provide security.

2. Can a bullet penetrate through a door?

Yes, a bullet can penetrate through a door if it has enough force and velocity. The type of material the door is made of, as well as the type of bullet and gun used, can also affect whether or not the bullet can penetrate through the door.

3. How does the angle of the bullet affect its impact on the door?

The angle of the bullet can greatly affect its impact on the door. If the bullet hits the door at a perpendicular angle, it is more likely to create a hole and penetrate through. However, if the bullet hits the door at an angle, it may ricochet off and cause less damage.

4. Can a door stop a bullet from a high-powered gun?

It depends on the type of door and the caliber of the bullet. Most doors are not designed to stop bullets from high-powered guns and may not provide enough protection. However, there are specialized bullet-proof doors that are specifically designed to withstand high-powered gunshots.

5. How does the thickness of the door affect its ability to stop a bullet?

The thickness of the door can greatly affect its ability to stop a bullet. Thicker doors made of stronger materials, such as metal or solid wood, are more likely to stop a bullet than thinner doors made of weaker materials, such as hollow wood or thin metal. However, the type of bullet and gun used can also play a role in whether or not the door can stop the bullet.

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