four particles connected by rigid rods of negligible mass where y1 = 5.70 m. the origin is at the center of the rectangle. The s

Question

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four particles connected by rigid rods of negligible mass where y1 = 5.70 m. the origin is at the center of the rectangle. The s

ystem rotates in the xy plane about the z axis with and angular speed of 5.60 rad/s. a) calculate the moment of inertia of the system about the z axis. b) Calculate the rotational kinetic energy

Physics

1 answer:

Sophie [7] · Answer 1 · 2022-08-20T04:11:43+03:00

The definition of moment of inertia and kinetic energy we can find the results for the questions are:

a) The moment of inertia is: I = 32.49 kg m²

b) The kinetic energy is: K = 509.4 J

a) The moment of inertia is a scalar quantity that has the same function as mass, it is given by

I = m r²

They indicate that the length of the bar is y₁ = 5.70 m, if the two rigid bars form the square that supports the masses, the distance from the center to the end where each mass is:

r = y₁ / 2

r = 5.70 / 2 = 2.85 m

The moment of inertia of the system is.

I = 4 m r²

Let's calculate.

I =4 m 2.85²

I = 32.49m kg m²

If we assume that the mass of each point particle is:

m = 1 kg

I = 32.49 kg m²

b) They ask for the rotational kinetic energy, if the angular velocity is.

w = 5.60 rad / s