68.6k views
0 votes
A particle of mass 0.500 kg is attached to the 100 -cm mark of a meterstick of mass 0.125 kg. The meterstick rotates on the surface of a frictionless, horizontal table with an angular speed of 2.00rad/s. (a) Calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 50.0-cm mark. (b) Calculate the angular momentum of the system when the stick is givoted about an axis perpendicular to the table through the 0 -cm mark.

User GlaIZier
by
7.5k points

1 Answer

2 votes

Final answer:

To calculate the angular momentum of the system, we need to consider the angular momentum of both the particle and the meterstick. The angular momentum of the particle is given by mvr, while the angular momentum of the meterstick is given by Iω. By adding these two angular momenta together, we can calculate the total angular momentum of the system for both pivot points.

Step-by-step explanation:

To calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 50.0-cm mark, we need to consider the angular momentum of both the particle and the meterstick.

The angular momentum of the particle is given by Lparticle = mvr, where m is the mass of the particle, v is its velocity, and r is the perpendicular distance from the axis of rotation. In this case, the particle is attached to the 100-cm mark, so the perpendicular distance is 50 cm or 0.5 m.

The angular momentum of the meterstick is given by Lmeterstick = Iω, where I is the moment of inertia of the meterstick and ω is its angular speed. The moment of inertia of a meterstick rotating about an axis perpendicular to its length at one end is given by I = (1/3)mL2, where m is the mass of the meterstick and L is its length.

To calculate the angular momentum of the system, simply add the angular momentum of the particle and the meterstick together: Lsystem = Lparticle + Lmeterstick.

To calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 0-cm mark, follow the same steps as above, but now the particle is attached to the 50-cm mark, so the perpendicular distance is 0.5 m.

User Wesww
by
7.9k points