Angular Momentum of wood door

[mvpshaq32]

Homework Statement

A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 41.0 kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.700 kg, traveling perpendicular to the door at 11.0 m/s just before impact.

Homework Equations

L=rmv=I(omega)

The Attempt at a Solution

I know I have to use conservation of momentum, but I have no idea how to set up the problem of turning linear momentum into angular momentum.

 

[rl.bhat]

You have to use conservation of linear and angular momentum.

 

[ashishsinghal]

You have to use conservation of linear and angular momentum.

you cannot use conservation of linear momentum. The hinge will provide external force.

 

[ashishsinghal]

I know I have to use conservation of momentum,

you have to use conservation of angular momentum.

but I have no idea how to set up the problem of turning linear momentum into angular momentum.

angular momentum = mvr sin(theta)

find angular momentum of door about the axis and multiply with angular velocity to get angular momentum.

 

[rwisz]

I would approach this problem by first identifying the key variables and principles involved. The key variables in this scenario are the mass and velocity of the mud, the mass and dimensions of the door, and the location and type of hinge. The principles involved include conservation of momentum and the relationship between linear and angular momentum.

To solve this problem, I would first calculate the initial linear momentum of the mud, which is given by the product of its mass and velocity (p=m*v). Then, using the principle of conservation of momentum, I would set this initial linear momentum equal to the final linear momentum of the system, which includes the door and the mud stuck to it.

Next, I would calculate the angular momentum of the door using the equation L=I*omega, where I is the moment of inertia and omega is the angular velocity. The moment of inertia for a rectangular object can be calculated using the formula I=(1/12)*m*(h^2+w^2), where m is the mass, h is the height, and w is the width. Since the door is initially at rest, the initial angular velocity is zero.

Then, I would use the principle of conservation of angular momentum to equate the initial angular momentum of the door to the final angular momentum, which includes the mud stuck to it. This would allow me to solve for the final angular velocity of the door.

Finally, I would use the relationship between linear and angular velocity (v=r*omega) to calculate the final linear velocity of the door, which would tell me how fast the door would be moving after the collision.

In summary, to solve for the angular momentum of a wood door struck by a handful of sticky mud, I would use the principles of conservation of momentum and conservation of angular momentum, along with the relationship between linear and angular momentum, to calculate the final angular velocity and linear velocity of the door.