A uniform rod of mass 2.10 kg and length 2.00 m is capable of rotating about an

Question

A uniform rod of mass 2.10 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 = 4.60 kg is attached to one end and a second mass m2 = 3.50 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 2.60 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 2.60 rad/s? J

Explanation / Answer

M = mass of rod = 2.10 kg

L = length of rod = 2 m

r = distance of each m1 and m2 from center = L/2 = 2 / 2 = 1 m

a)

I = moment of inertia of rod and mass m1 and m2 = (1/12) ML2 + (m1 + m2) r2

I = (1/12) (2.10) (2)2 + ((4.60) + (3.50)) (1)2 = 8.8 kgm2

b)

w = angular speed = 2.60 rad/s

kinetic energy = (0.5) I w2 = (0.5) (8.8) (2.60)2 = 29.74 J

c)

I = moment of inertia = (m1 + m2) r2 = ((4.60) + (3.50)) (1)2 = 8.1 kgm2

d)

kinetic energy = (0.5) I w2 = (0.5) (8.1) (2.60)2 = 27.4 J

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