Solve with given values A pendulum consists of a slender rod, AB , of weight W r

Question

Solve with given values
A pendulum consists of a slender rod, AB, of weight Wr = 9.50lb and a wooden sphere of weight Ws = 24.6lb .(Figure 1) The length of the rod is d1 = 7.20ft and the radius of the sphere is R = 0.450ft . A projectile of weight Wp = 0.500lb strikes the center of the sphere at a velocity of v1 = 921ft/s and becomes embedded in the center of the sphere. What is ?, the angular velocity of the pendulum, immediately after the projectile strikes the sphere? Express your answer numerically in radians per second to three significant figures. Solve with given values
A pendulum consists of a slender rod, AB, of weight Wr = 9.50lb and a wooden sphere of weight Ws = 24.6lb .(Figure 1) The length of the rod is d1 = 7.20ft and the radius of the sphere is R = 0.450ft . A projectile of weight Wp = 0.500lb strikes the center of the sphere at a velocity of v1 = 921ft/s and becomes embedded in the center of the sphere. What is ?, the angular velocity of the pendulum, immediately after the projectile strikes the sphere? Express your answer numerically in radians per second to three significant figures.

Explanation / Answer

Conservation means the magnitude (i.e. if its a vector quantity like momentum then the root of the sum of the square of the separate components) must be constant and un-changing at all points in motion.

Momentum in this case is not conserved because it is changing with respect to t, x, and y.

Energy, however, is conserved. The key thing is that total energy E = K+U must be conserved, which it is as long as the force field is conservative, etc.

Potential energy conservation and kinetic energy conservation would be very specific limiting cases. For instance, in the case of linear momentum conservation from something like impact, kinetic energy is conserved (when there is no lost energy due to impact). I'm not sure but perhaps kinetic energy is conserved when momentum is conserved. Potential energy conservation just means there's no change in motion or inertia (think Newton's first law sorta).

But, what matters, is that total energy E is conserved. For a rigorous mathematical background of this, just see Noether's Theorem. hope this helps.

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