The figure below shows a rigid structure consisting of a circular hoop of radius

Question

The figure below shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 6.2 s.

(a) Assuming R = 0.20 m and m = 6.0 kg, calculate the structure's rotational inertia about the axis of rotation.

__________________________ kg m2

(b) What is its angular momentum about that axis?

___________________________ kg m2/s

The figure below shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 6.2 s. (a) Assuming R = 0.20 m and m = 6.0 kg, calculate the structure's rotational inertia about the axis of rotation. __________________________ kg m^2 (b) What is its angular momentum about that axis? ___________________________ kg m^2/s

Explanation / Answer

a) moment of inertia of square = 2 x m x R^2 /3 + mR^2 = 5mR^2/3

moment of inrtia of hoop = mr^2/2 + mr^2 = 3mR^2 /2

total moment of inertia = 19mR^2 /6

= 19 x 6 x 0.2^2 /6 = 0.76 kg.m^2

b)

T = 2xpi / w

w =2 x pi / 6.2 =1.01 rad/s

angular moemntum = Iw = 0.76 x 1.01 = 0.77 kg.m^2/s

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