Angular momentum of rigid bodies,When to add (moment of inertia*angular velociy)

In summary, the 30-lb plank is struck by a 15-lb hammer with a vertical velocity of 75 ft/s. The coefficient of restitution between the hammer head and the plank is 0.5. The 50-lb block D is able to slide freely along two vertical guide rods. The maximum height attained by the block D can be determined by applying the conservation of angular momentum theorem to the system, taking into account the moment of inertia of the plank as it rotates.
  • #1
tj00343
63
0
The rigid 30-lb plank is struck by the 15-lb hammer
head H. Just before the impact the hammer is gripped
loosely and has a vertical velocity of 75 ft>s. If the coefficient
of restitution between the hammer head and the plank is
e = 0.5, determine the maximum height attained by the 50-lb
block D. The block can slide freely along the two vertical
guide rods. The plank is initially in a horizontal position.

link to diagram :
http://s3.amazonaws.com/answer-board-image/cc993076-7bbb-4ab8-936b-9788a74b8565.png

I applied the conservation of angular mom. thm, but after checking the solution manual ,
I realized that they applied the thm but adding for the whole system ,they took for the plank ,hammer, and block, m(Vg)*(distance to point B) , BUT (this is my real quistion ) ,for the plank they did , [m(Vg)*(distance to point B)] +[Ig*w] ...my quistion is why was'nt the Igw term added for the block and hammer ,and why was it added to the plank
 
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  • #2
only The answer is that the hammer and block are not rotating, so the moment of inertia is zero. The plank is rotating, so it has a moment of inertia, which must be taken into account when calculating its angular momentum.
 

1. What is angular momentum of a rigid body?

Angular momentum of a rigid body is a measure of the amount of rotational motion that a body possesses. It is a vector quantity that takes into account the mass, shape, and angular velocity of the object.

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia (a measure of an object's resistance to rotational motion) by the angular velocity (the rate at which the object is rotating).

3. Why is the moment of inertia important in calculating angular momentum?

The moment of inertia is important because it takes into account the distribution of mass in an object and how it affects its rotational motion. Objects with a larger moment of inertia require more torque to rotate at a given angular velocity, resulting in a greater angular momentum.

4. When should the moment of inertia be added to the angular velocity?

The moment of inertia should be added to the angular velocity when calculating the angular momentum of a rigid body that is rotating about a fixed axis. This is because the moment of inertia and angular velocity are both vectors and must be added according to the rules of vector addition.

5. Can the angular velocity change without affecting the angular momentum?

No, the angular momentum of a rigid body is conserved, meaning it cannot be created or destroyed. Therefore, any change in the angular velocity will result in a corresponding change in the moment of inertia to maintain the same angular momentum.

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