A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an

Question

A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass

m1 = 4.90 kg

is attached to one end and a second mass

m2 = 3.10 kg

is attached to the other end of the rod. Treat the two masses as point particles.

(a) What is the moment of inertia of the system?
_______kg · m2

(b) If the rod rotates with an angular speed of 2.40 rad/s, how much kinetic energy does the system have?
_______J

(c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined?
_______kg · m2

(d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.40 rad/s?
_______J

Explanation / Answer

(a) I = ML²/12 + m(L/2)²

where m is m1+m2

and M is the mass of the rod.

I = 1.9kg * (2.00m)² / 12 + (4.9 + 3.1)kg * (1.00m)² = 8.6333 kg·m²

(b) KE = ½I² = ½ * 8.6333kg·m² * (2.40rad/s)² = 24.864 J

(c) I' = (4.9 + 3.1)kg * (1.00m)² = 8 kg·m²

(d) KE' = ½ * 8kg·m² * (2.40rad/s)² = 23.04 J

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