Part C please To be able to describe the motion of rigid bod

Part C please!

To be able to describe the motion of rigid bodies by applying the conservation of linear and angular momenta. If the sum of all the linear impulses acting on a system of connected rigid bodies is zero, the linear momentum of A pendulum consists of a slender rod, AB, of weight WT = 8.00 lb and a wooden sphere of weight W_r = 24.6 lb .(Figure 1) The length of the rod is d_1 = 8.90 ft and the radius of the sphere is R = 0.200 ft. A projectile of weight W_p = 0.400 lb strikes the center of the sphere at a velocity of V_1 =914 ft/s and becomes embedded in the center of the sphere. What is to, the angular velocity of the pendulum, immediately after the projectile strikes the sphere? What is theta, the maximum angle measured from the vertical that the pendulum will swing, after the projectile impacts the pendulum?

Solution

If part B is correct then you have corrrectly found moment of inertia

Now you have to apply work energy theorem

Let at bottom level potential energy is 0 and final potential energy iis

P.E = W_t*(d₁/2)*(1-cos(theta)) + (W_s + W_p)*(d₁ + R)*(1-cos(theta)) ;

final kinetic energy is 0.

initial K.E = 0.5*I*w²

apply work energy theorem

0.5*I*w² = W_t*(d₁/2)*(1-cos(theta)) + (W_s + W_p)*(d₁ + R)*(1-cos(theta))