Question

The rod of length l is heated to 180 watts to the horizontal position, which releases it with angular velocity when its particle position is:

a) At the center
b) At the end
c) At 45 degrees
d) At 90 degrees

Answer 1

The angular velocity of a rod depends on its moment of inertia and initial conditions of its particle's position. Therefore the correct answer is c) At 45 degrees.

Step-by-step explanation:

The angular velocity of a rod is determined by its moment of inertia and angular momentum. When the rod is released from rest, its angular velocity depends on the initial conditions, such as the position of its particle.

In this case, if the particle is at the center of the rod, it will have an angular velocity of 10.0 rad/s. If the particle is at the end, the angular velocity will be higher. At 45 degrees and 90 degrees, the angular velocity will also depend on the initial conditions of the particle.

The angular velocity of a rotating object like a rod or pendulum changes as the distribution of mass changes or as external forces act on the system. This concept is essential in understanding rotational dynamics and its conservation in closed systems.

For example, when the catches are released in the uniform rod scenario, the beads slide outwards altering the moment of inertia and, as a result of angular momentum conservation, affecting the angular velocity. Calculating this requires understanding of the conservation of angular momentum.