Question

what is the angular momentum vector of the 2.0 kg , 4.0- cm -diameter rotating disk in (figure 1)? give your answer using unit vectors.

Answer 1

The angular momentum vector (L) of a rotating disk can be calculated using the formula L = I\(\omega\). For a disk of mass 2.0 kg and a 4.0-cm diameter, and assuming unit angular velocity vector in the z-direction, the angular momentum vector is L = (0.0004 kg\(\cdot\)m^2)\(\omega\)k, pointing along the axis of rotation in the direction given by the right-hand rule.

Step-by-step explanation:

To determine the angular momentum vector of a rotating disk, we should follow the following steps:

For a disk of mass 2.0 kg and diameter 4.0 cm (radius 2.0 cm or 0.02 m), the moment of inertia is given by I = (1/2)mR^2. Since the problem does not provide the angular velocity, we can assume a unit angular velocity vector perpendicular to the plane of rotation if the rotation axis is through the center of the disk. Using the right-hand rule, the direction will typically be along the z-axis, assuming the disk lies in the xy-plane.

The moment of inertia I = (1/2)(2.0 kg)(0.02 m)^2 = 0.0004 kg\(\cdot\)m^2.

If we assume unit angular velocity vector in z-direction, then \(\omega\) = \(\omega\)k, and thus:

L = I\(\omega\)k = (0.0004 kg\(\cdot\)m^2)\(\omega\)k

The direction of the angular momentum vector L will be along the axis of rotation determined by the right-hand rule, which for a typical counterclockwise rotation as viewed from above, would be in the positive z-direction.

Answer 2

The angular momentum vector for a rotating disk with a mass of 2.0 kg and a diameter of 4.0 cm can be calculated using the moment of inertia and the angular velocity. The direction is perpendicular to the plane of rotation, determined by the right-hand rule.

Step-by-step explanation:

The question pertains to the calculation of the angular momentum vector for a rotating disk. The mass of the disk is 2.0 kg and its diameter is 4.0 cm, which gives it a radius of 2.0 cm or 0.02 meters. To calculate the angular momentum vector, we need to determine the disk's moment of inertia (I) and its angular velocity (ω).

The moment of inertia for a solid disk rotating about an axis through its center is given by I = 0.5 ⋅ m ⋅ r², where m is the mass and r is the radius. The angular velocity is not specified in the question, so it cannot be calculated without additional information.

Assuming we had an angular velocity ω, the angular momentum L would be calculated using the formula L = I υ ω. The direction of the angular momentum vector is determined by the right-hand rule and is perpendicular to the plane of rotation. If the disk is rotating counterclockwise when viewed from above, the angular momentum vector would point upwards along the axis of rotation.