Question

A bicycle wheel of mass M and radius R is placed on a vertical axle and is able to rotate without friction. A dart of mass, m is fired toward the wheel with an initial velocity v(o). The dart strikes the wheel and sticks in the tire. The moment of inertia of the wheel is I=mr^2. What is the initial angular momentum of the dart with respect to the center of the wheel? What is the angular velocity of the wheel after the dart strikes?

Answer 1

===>

the initial angular momentum of the dart with respect to the center of the wheel is

= m V_o R sin$\theta$

and

===>

the angular velocity of the wheel after the dart strikes is

=> m V_o R sin$\theta$ = R² ( M + m ) $\omega$

m V_o sin$\theta$ = R ( M + m ) $\omega$

$\omega$ = m V_o sin$\theta$ / R ( M + m )