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 = 5.00 kg is attached to one end and a second mass m2 = 3.30 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?
Answer in kg · m2

(b) If the rod rotates with an angular speed of 2.00 rad/s, how much kinetic energy does the system have?
Answer in J

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

(d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.00 rad/s?
Answer in J

Explanation / Answer

a)

I_rod = m1L^2 /12

          = 1.9*2^2 /12

          = 0.63 kg-m^2

I_p1 = m1r^2

       = 5.0*(2/2)^2

      = 5.0 kg-m^2

I_p2 = m2r^2

      = 3.3*(2/2)^2

      = 3.3 kg-m^2

Total MOI = 0.63 + 5 + 3.3

                 = 8.93kg-m^2

b)

KE = 1/2* I*w^2

      = 1/2 * 8.93* 2^2

      = 17.86 J

c)

I = 0 + 5 + 3.3

= 8.3 kg-m^2

d)

KE = 1/2 * I *w^2

      = 1/2*8.3 *2^2

     = 16.6J

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