# A bullet of mass

Given:

Mass of Bullet, m = 10g = 10-3 kg

Speed of bullet, v = 500m/s

Width of the door, w = 1m

Distance from hinge where bullet hits, r = 0.5 m

Mass of door, M = 12 Kg

We know that angular moment is given by,

α = mvr

where,

α = angular momentum

m = mass of the body

v = velocity of the body

r = radius of the body

by putting the value, we get,

α = 10 × 10-3 kg × 500 ms-1 × 0.5 m

α = 2.5 Kgm2s-1 …(i)

Moment of inertia is given by,

I = ML2/3 (For rectangle)

Where,

M = mass of door

L = width of door

I = 1/3 × 12 Kg × (1m)2

I = 4 Kgm2

We also have,

α = Iω

where is α is the angular momentum

l is the linear momentum

ω is the angular velocity

ω = α /I

By putting the values, we get,

ω = 2.5/ 4

Note: It is a good practice to memorise the moment of inertia for common shapes like rectangle, circle, triangle, cylinder and sphere.

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