A rod of mass M and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving with speed V, strikes the rod at angle θ from the normal and sticks to the rod after the collision. show answer No Attempt 50% Part (a) What is the total moment of inertia, I, with respect to the hinge, of the rod-ball-system after the collision?

  I_total = L² (m + M / 3)

Explanation:

The moment of inertia is defined by

        I = ∫ r² dm

It is appreciated that it is a scalar quantity, for which it is additive, in this case the system is formed by two bodies and the moment of inertia must be the sum of each moment of inertia with respect to the same axis of rotation.

The moment of inertia of a bar with respect to an axis that passes through ends is

            I_bar = 1/3 M L²

The moment of inertia of a particle is

           I_part = m x²

We have to assume the point where the particle sticks to the bar, suppose it sticks to the end

              x = L

Total moment of inertia is the sum of these two moments of inertia

          I_total = I_bar + I_particule

          I_total = 1/3 M L² + m L²

         I_total = L² (m + M / 3)

i guess it’s a and b

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !