Question 1 The figure shows a rigid assem bly of a thin hoop (of mass m = 0.24 k

Question

Question 1 The figure shows a rigid assem bly of a thin hoop (of mass m = 0.24 kg and radius R·O.12 m) and a thin radial rod of lerg L-29 and iso of mass m = 0.24 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? Hoop Rod Rotation axis Number Units the tolerance is +/-2%

Explanation / Answer

Icm of hoop = m r^2 / 2

about rotation axis, I1 = (m r^2 / 2) + m (L+r)^2

= 0.24( 0.12^2 /2 + (0.12 + 0.24)^2 )

= 0.0346 kg m^2

of rod, I2 = m L^2 / 3 = (0.24) (0.24^2)/3

I2 = 4.61 x 10^-3 kg m^2

I = I1 + I2 = 0.0392 kg m^2

Applying energy conservation,

PEi + KEi = PEf + KEf

((0.24 x 0.12 x 9.8) + (0.24 x 0.36 x 9.8)) + 0 = (0.0392 w^2 / 2) - ((0.24 x 0.12 x 9.8) + (0.24 x 0.36 x 9.8))

w = 10.7 rad/s

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