Figure 11-45 shows a rigid structure consisting of a circular hoop of radius R a

Question

Figure 11-45 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 2.3 s. If R = 1.2 m and m = 3.2 kg, calculate the angular momentum about that axis.

Figure 11-45 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 2.3 s. If R = 1.2 m and m = 3.2 kg, calculate the angular momentum about that axis.

Explanation / Answer

Moment of inertia of the square: mR2 + 2/3mR2 = 5/3 mR2 Moment of inertia of hoop = mR2/2 + mR2 = 3/2mR2 Total inertia = 19/6mR2 Angular velocity = 2pi/2.3 = 2.73 rad/sec Angular momentum = 2.73*19/6mR2 = 8.65mR2 = 39.84 kgm2rad/sec

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