Ahorizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. the platform has a mass of 117.0 kg, a radius of 2.00 m, and a rotational inertia of 4.68×102 kgm2 about the axis of rotation. a student of mass 50.0 kg walks slowly from the rim of the platform toward the center. if the angular speed of the system is 1.75 rad/s when the student starts at the rim, what is the angular speed when she is 0.650 m from the center? 2.98 rad/s

2.39 rad/sec

Explanation:

Under the assumption that no external torques are applied, total angular momentum must be conserved:

L₁ = L₂

The initial angular momentum, is given by the following expression:

L₁ = I₁ ω₁ , where I₁, is the total rotational inertia  of the system, and is equal to the sum of the rotational inertia of the disk, plus the one due to the student standing just in the rim of the disk, as follows:

I₁ = Id + Is = 4.68.10² Kg m² + 50.0 (2.00) ² kg.m²= 668 Kg.m²

So, L₁ = 668 kg. m² . 1.75 rad/s = 1,169 Kg.m². rad/s

Final angular momentum, is obtained as follows:

L₂ = I₂ . ω₂.

Now, I₂, is just the same term as in I₁, with the difference, that Is now given by the following expression:

Is₂ = 50. 0 . (0.65)² kg.m² = 21.1 kg.m²

So, total I₂ is as follows:

I₂ = 468 kg. m² + 21.1 kg.m² = 489.1 Kg.m²

So, equating L₁ and L₂, and solving for ω₂, we have:

489.1 Kg. m² . ω₂ = 1,169 kg. m² rad/sec ⇒ ω₂ = 2.39 rad/sec

it takes about 30 days for it to break down

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force