Centre of Mass and Moment of Inertia (1 point) 2 An object is made of 2 identica
ID: 3308207 • Letter: C
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