Question

a bullet fired from the muzzle of a rifle initially rotates with an angular velocity of 2200 radians per second.If the bullet is slowed by friction and rotates through 480 revolutions during its 1.4 seconds of flight,find the tangential acceleration of the bullet

Answer 1

Initial angular speed of the bullet is 2200 rad/s

after some time the angular speed of bullet is decreased and it rotates through 480 revolutions in 1.4 s

so the angle revolved by the bullet is

`\theta = 2 N\pi`

`\theta = 2*480*\pi= 3016 radian`

now the angular acceleration is given as

`\theta = \omega_0*t +(1)/(2)\alpha t^2`

`3016 = 2200* 1.4 + (1)/(2)*\alpha* 1.4^2`

`3016 = 3080 + 0.98 \alpha`

`\alpha = - 65.3 rad/s^2`