Centre of Mass and Moment of Inertia (1 point) 2 An object is made of 2 identica

Question

Centre of Mass and Moment of Inertia (1 point) 2 An object is made of 2 identical thin rods with length L = 17.5 cm and mass m = 200 g. At the end of each rod is a solid sphere with diameter d = 4.50 cm and mass M = 600 g. The rods are attached to the surface of the spheres. The rods are joined at the origin O and each makes an angle = 30° with the z-axis as shown The object is initially at rest. A constant torque of 0.100 Nm along the z-axis is applied for 2.00 s. lgnoring friction, how many revolutions per minute does the object make after this? Enter the number of revolutions per minute (rpm).

Explanation / Answer

Icm of sphere = 2 M d^2 / 20

Icm of rod = m L^2 / 12

and I = Icm + m r^2

hence total moment of inertia of system about the pivot point P,

Ip = 2 [ 2 M d^2 / 20 + M (L + d/2)^2] + 2[ m L^2 / 12 + m (L/2)^2]

putting values,

M = 0.600 kg , d = 0.0450 m , L = 0.175 m, m = 0.200 kg

Ip = 0.05114 kg m^2

Applying torque = I alpha

0.100 = 0.05114 alpha

alpha = 1.96 rad/s^2

w = w0 + alpha t

w = 0 + (1.96 x 2) = 3.911 rad/s

w (in rpm) = 3.911 (1/2pi) rev / (1/60)m

= 37.35 rpm

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