Youre feeling particularly lazy and decide to open a door by

You\'re feeling particularly lazy and decide to open a door by firing a bullet at it. The door has a mass of 9.50 kg and is 0.800 m wide, and the 10 g bullet, traveling at 350. m/s, hits the door at the edge opposite the hinges. The bullet stops inside the door, which then swings open.

What is the angular velocity of the door just after the bullet hits it?

Solution

Here ,

mass of bullet , m = 10 gm

m = 0.010 kg

speed of bullet , u = 350 m/s

mass of door , M = 9.5Kg

length of door , L = 0.8 m

let the final angular speed of the door is w

Using conservation of angular momentum

I * w = m * v * r

(M * L^2/12 + m *L^2) * w = m * v * r

(9.5 * 0.8^2/12 + 0.010 * 0.8^2) * w = 0.010 * 350 * 0.8

solving for w

w = 5.46 rad/s

the angular speed of the door is 5.46 rad/s