The free precession rate of the symmetry axis (the 3-axis) with of a rigid body,

Question

The free precession rate of the symmetry axis (the 3-axis) with of a rigid body, as viewed from the space frame is where alpha is the angle of the symmetry axis with respect to the angular velocity vector w. (a)Show that for a free spinning uniform flat disk, when a is small, the precession rate is approximately twice that of its spin rate. (b) For a free spinning thin uniform rod (i.e., its radius is much smaller than its length), the precession rate of the symmetry axis is 0.01 that of the spin rate. Approximately what is the angle alpha, in radians? [10 points]

Explanation / Answer

The formula for recoil velocity is Mass of gun*Speed of Gun = Mass of Bullet*Speed of Bullet

We are given mass of gun=5.7kg=5700

mass of bullet =12g

speed of gun= we have to find

speed of the bullet when fired= we have to find

we are given with s= 1000m final velocity of bullet=299m/s and accerlation= -1m/s^2

u will be intial velocity of bullet

We know v^2-u^2=2as

299^2-u^2=2(-1)(1000)

89401+2000=u^2

91401=u^2

302.3m/s=u

Mass of gun*Speed of Gun = Mass of Bullet*Speed of Bullet

5700*Speed of gun=12*302.3

5700*Speed of gun=3627.6

Speed of gun=3627.6/5700

Speed of gun=0.636m/s

Which is the recoil velocity =0.636

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