Yesterday you saw in the news that the Giant Asian Murder Hornet has migrated to North America. You didn't think much about it until today when one of those suckers crashed at high speed into the screen door at the back of your house (splat!). The thing hit the door so hard that the door swung shut! We will assume that GAMH had a mass of m = 0.064 kg and was moving with an amazing velocity of v = 6.4 meters/second. The GAMH splatted a distance d = 0.68 meters from the hinge. The door itself can be treated as a rod of mass M = 1.089 kg with a length of L = 0.92 meters rotating about its end. Determine all the following: a) Write the FORMULA for the moment of inertia of the door without the hornet: I = kg m2 b) Write the FORMULA for the moment of inertia of the door with the hornet: I = kg m2 c) Determine the angular momentum of the hornet before it collides with the door Lhornet = kg m2/s d) Determine the angular velocity of the hornet-stained door after the collision ?2 = rad/sec e) Determine the time required for the door to close: t(? = ?/2) = seconds
Yesterday you saw in the news that the Giant Asian Murder Hornet has migrated to North America. You didn't think much about it until today when one of those suckers crashed at high speed into the screen door at the back of your house (splat!). The thing hit the door so hard that the door swung shut! We will assume that GAMH had a mass of m = 0.064 kg and was moving with an amazing velocity of v = 6.4 meters/second. The GAMH splatted a distance d = 0.68 meters from the hinge. The door itself can be treated as a rod of mass M = 1.089 kg with a length of L = 0.92 meters rotating about its end. Determine all the following: a) Write the FORMULA for the moment of inertia of the door without the hornet: I = kg m2 b) Write the FORMULA for the moment of inertia of the door with the hornet: I = kg m2 c) Determine the angular momentum of the hornet before it collides with the door Lhornet = kg m2/s d) Determine the angular velocity of the hornet-stained door after the collision ?2 = rad/sec e) Determine the time required for the door to close: t(? = ?/2) = seconds
Yesterday you saw in the news that the Giant Asian Murder Hornet has migrated to North America. You didn't think much about it until today when one of those suckers crashed at high speed into the screen door at the back of your house (splat!). The thing hit the door so hard that the door swung shut! We will assume that GAMH had a mass of m = 0.064 kg and was moving with an amazing velocity of v = 6.4 meters/second. The GAMH splatted a distance d = 0.68 meters from the hinge. The door itself can be treated as a rod of mass M = 1.089 kg with a length of L = 0.92 meters rotating about its end. Determine all the following: a) Write the FORMULA for the moment of inertia of the door without the hornet: I = kg m2 b) Write the FORMULA for the moment of inertia of the door with the hornet: I = kg m2 c) Determine the angular momentum of the hornet before it collides with the door Lhornet = kg m2/s d) Determine the angular velocity of the hornet-stained door after the collision ?2 = rad/sec e) Determine the time required for the door to close: t(? = ?/2) = seconds
Yesterday you saw in the news that the Giant Asian Murder Hornet has migrated to North America. You didn't think much about it until today when one of those suckers crashed at high speed into the screen door at the back of your house (splat!). The thing hit the door so hard that the door swung shut! We will assume that GAMH had a mass of m = 0.064 kg and was moving with an amazing velocity of v = 6.4 meters/second. The GAMH splatted a distance d = 0.68 meters from the hinge. The door itself can be treated as a rod of mass M = 1.089 kg with a length of L = 0.92 meters rotating about its end.
Determine all the following: a) Write the FORMULA for the moment of inertia of the door without the hornet: I = kg m2 b) Write the FORMULA for the moment of inertia of the door with the hornet: I = kg m2 c) Determine the angular momentum of the hornet before it collides with the door Lhornet = kg m2/s d) Determine the angular velocity of the hornet-stained door after the collision ?2 = rad/sec e) Determine the time required for the door to close: t(? = ?/2) = seconds
Transcribed Image Text:The diagram depicts a physics problem involving rotational motion. It shows a wasp, with mass "m" and velocity "v," moving towards a vertical rod.
**Diagram Explanation:**
- The wasp is moving horizontally with velocity "v" towards the rod.
- The vertical rod is anchored at the top with a hinge. The hinge allows the rod to rotate.
- The length of the rod is "L," and its mass is "M."
- The point of impact from the wasp on the rod is "d" away from the hinge.
- The problem asks to determine the time "t" it takes for the rod to rotate to a horizontal position, at an angle \(\theta = \frac{\pi}{2}\).
The goal is to find the time "t" for the rotational motion of the rod after the wasp impacts it.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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