A slender rod with length L has a mass per unit length that varies with distance...

A slender rod with length L has a mass per unit length that varies with distance from the left

end, where ? = 0, according to ??/?? = ??, where ? has units of kg/m^2

a. Calculate the total mass M of the rod in terms of ? and L.

b. Use the equation ? = ∫ ?=?? to calculate the moment of inertia of the rod for an axis at the left

end, perpendicular to the rod. Express your result in terms of M and L.

c. Assume that the rod with length ? = 0.4 ? and mass M = 3.0 kg is rotating about the axis as in part b. The angle through which the rod has turned varies with time according to

?(?) = (1.1 rad/s)t + (6.3 rad/s^2)t^2. What is the kinetic energy of the rod when it has

rotated 0.1 rev?

part c only

Expert Solution

genius_generous answered 2 years ago

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