A 223 bullet is propelled in a barrel that has a twist rate

A .223 bullet is propelled in a barrel that has a twist rate of one in 9 inches. The bullet weighs 55 grains, its outer diameter is 0.224 in, its radius of gyration is 0.08 in, and the muzzle velocity is 3100 fps. Determine the kinetic energy of the bullet associated with its angular motion.

Solution

Linear velocity 3100 ft per sec.

3100 X 12 inches/sec

The projectile turns once every 9 inches, hence for 3100*12 inches it turns 3100*4/3 times, or 4133.3 revs/sec

This is Pi*4133.3 radians/sec ( 1rev =2pi radiams)

Moment of inertia of bullet is 1/2 MK²

M is mass, K is radius of gyration

Mass is 55 grains = 55* 64.799 mg

KE = 1/2 * 55*64.8/ 1000 * ( .08*2.54/100)^2 gm m²* ( 2pi* 4133.3)^2

in terms of kg divide by 1000 again

get approx 1.2 x10⁹ J