# Answer in Physics for Irish #162868

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

1. Blu-ray disc (inner diameter 0.015 m, outer diameter 0.120 m, mass 0.016 kg)

spinning at a rate of 10,000 rpm

2. 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.

3. Bicycle wheel with mass 2.0 kg and diameter 0.63 m rotating at a rate of 2.00

rpm. Assume that the bicycle wheel is a thin-walled hollow cylinder.

1. The moment of inertia:

“I = mdfrac{r_1^2 + r_2^2}{2}\nI = 0.016cdot dfrac{0.015^2 + 0.120^2}{2} = 1.17times 10^{-4}kgcdot m^2”

The angular frequency:

“omega = 2pidfrac{10000}{60} approx 1047.2space rad/s”

The angular momentum:

“L = Iomega\nL = 1.17times 10^{-4}cdot 1047.2 approx 0.12space kgcdot m^2/s”

2. The moment of inertia:

“I = 4times mdfrac{w^2}{3}\nI = 4times 20cdot dfrac{1.75^2}{3} approx 81.67space kgcdot m^2”

The angular frequency:

“omega = 2pidfrac{8}{60} approx 0.84space rad/s”

The angular momentum:

“L = Iomega\nL approx 68.4space kgcdot m^2/s”

3. The moment of inertia:

“I = mr^2\nI = 2cdot (0.63/2)^2 =0.19845 space kgcdot m^2”

The angular frequency:

“omega = 2pidfrac{2}{60} approx 0.21space rad/s”

The angular momentum:

“L = Iomega\nL approx 0.042space kgcdot m^2/s”

Answer. 1) 0.12 kg*m^2/s, 2) 68.4 kg*m^2/s, 3) 0.042 kg*m^2/s.

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