Answer to Question #162871 in Physics for Vic

Question

Calculate the angular momentum of the following systems. Refer to Worksheet 19 for the

moment of inertia of highly-symmetric objects. For all items, you need to convert from

rpm to rad/s first.

Revolving door with four wings, each with mass 20.0 kg, rotating at a rate of 8

rpm. Each wing can be considered to be a single door with height 3.00 m and

width 1.75 m.

Answer 1

8 rpm is 0.133 rad/s, or

$$\omega=2\pi n=0.838\text{ rad/s}.$$

We can consider each pair of oppositely located wings as a rectangle of width 3.5 m, height 3 m, and vertical axis of rotation at 1.75 m. Thus, the angular momentum will be

$$L=I\omega,\\\space\\ I=2\cdot\frac{1}{12}m(w^2+h^2)=\\\space\\ =2\cdot\frac{1}{12}· 20(3^2+3.5^2)=\\\space\\70.8\text{ kg m}^2.\\\space\\ L=70.8\cdot0.838=59.3\text{ kg}·\text{m/s}^2.$$