A uniform, 4.5 kg, square, solid wooden gate 1.5 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 5.0 m/s flies into this door at its center and bounces back at 2.5 m/s in the opposite direction..What is the angular speed of the gate just after it is struck by the unfortunate raven?

ω = 1.82 rad/sec

Explanation:

Given

mass of the gate = 4.5 kg

distance between the hinge 1.5 m

mass of the bird = 1.2kg

velocity of the bird = 5 m/s  

The gate is rotates in circular motion

Inertia ot the gate = ×m×r²

                            =  ×4.5×1.5²

                               = 3.3 kg/m²---------(1)

momentum of the the rave = mv

                                       = 1.2×5

                                       = 6.0 kg

angular momentum of the gate = Iω

By conservation of energy

6. 0= 3.3×ω

ω= 6.0/3.3

= 1.82 rad/sec

from equation 1

I = 3.3 kg/m^2

ω = 1.82 rad/sec

answer: the correct answer id option(d).

explanation:

snell's law refraction:

the angle of refraction =

the angle of incidence =

refractive index of air = = 1

refractive index of glycerol = 1.47

from the given options, the most closest answer to 63.72° is 65° of option (d).

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.