arsmaer for the Earth to go once around the Sun longe o rotate once about its ax

Question

arsmaer for the Earth to go once around the Sun longe o rotate once about its axis cantlh ures signiti- mass 0.400 kg is attached to the 100-cm i particle of ar 0.40 stick of mass 0.100 kg. The metersticl able with an angular speed of 4.00 rad/s. Calenlas he angular momentum of the system when the stic is pivoted about an axis (a) perpendicular to the tacle through the 50.0-cm mark and (b) perpendicular to rotates on the surface of a frictionless, horizontal the table through the 0-cm mark. The distance between the centers of the wheels of a

Explanation / Answer

Angular momentum is p = I*, where I is the moment of inertial about the axis of rotation. The problem comes down to calculating the moment of inertial of the system.

a)

Moment of inertia of the particle = 0.400*(1.00 - 0.50)² = 0.1 kg-m²

The moment of inertia of the meter stick about its center of mass (50 cm point) is m*L²/12

I(meter stick) = (0.100)(1)^2/12 = 0.00833 kg-m²

The total moment of inertia is then 0.1 + 0.00833 = 0.10833 kg-m²

The angular momentum is then Iw = 0.10833*4 = 0.43332 kg-m²/s

b)

The moment of inertia of the meter stick about its end (0 cm point) is m*L²/3

I(meter stick) = (0.100)(1)^2/3 = 0.0333 kg-m²

The total moment of inertia is then 0.1 + 0.0333 = 0.1333 kg-m²

The angular momentum is then Iw = 0.1333*4 = 0.5333 kg-m²/s

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