Question

A uniform, 4.5 kg, square, solid wooden gate 2.0 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.2 kg raven flying horizontally at 4.5 m/s flies into this door at its center and bounces back at 1.5 m/s in the opposite direction. What is the angular speed of the gate just after it is struck by the unfortunate raven?

Answer 1

The angular speed of the gate just after it is struck by the raven is 0 rad/s.

Step-by-step explanation:

To find the angular speed of the gate just after it is struck by the raven, we can use the principle of conservation of angular momentum. The initial angular momentum of the system is zero, since the gate is at rest. When the raven hits the gate, it transfers some of its angular momentum to the gate. The final angular momentum of the system can be calculated as:

Initial Angular Momentum of Raven = Final Angular Momentum of Gate

Since the raven bounces back, its final angular momentum is zero. Therefore, the final angular momentum of the gate is also zero. Using the formula for angular momentum, we can solve for the angular speed of the gate:

Angular Momentum = Moment of Inertia * Angular Speed

Since the gate is a square, solid wooden gate, its moment of inertia can be calculated using the formula for a square plate:

Moment of Inertia = (1/6) * Mass * Side Length^2

Plugging in the values given in the question:

Mass = 4.5 kg

Side Length = 2.0 m

Using these values, we can calculate the moment of inertia:

Moment of Inertia = (1/6) * 4.5 kg * (2.0 m)^2 = 6.0 kg·m²

Since the final angular momentum is zero, we can rearrange the formula for angular momentum to solve for the angular speed:

Angular Speed = 0 / Moment of Inertia = 0 rad/s