A horizontal 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 radius of 2.97 m and a rotational inertia of 358 kg·m2 about the axis of rotation. A 69.5 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.96 rad/s when the student starts at the rim, what is the angular speed when she is 1.06 m from the center?

4.36 rad/s

Explanation:

Radius of platform r = 2.97 m

rotational inertia I = 358 kg·m^2

Initial angular speed w = 1.96 rad/s

Mass of student m = 69.5 kg

Rotational inertia of student at the rim = mr^2 = 69.5 x 2.97^2 = 613.05 kg.m^2

Therefore initial rotational momentum of system = w( Ip + Is)

= 1.96 x (358 + 613.05)

= 1903.258 kg.rad.m^2/s

When she walks to a radius of 1.06 m

I = mr^2 = 69.5 x 1.06^2 = 78.09 kg·m^2

Rotational momentuem of system = w(358 + 78.09) = 436.09w

Due to conservation of momentum, we equate both momenta

436.09w = 1903.258

w = 4.36 rad/s

this allows people to make the best decision or pursue the best option. when alternatives are weighed using their advantages and disadvantages, the option whose disadvantages outweigh the advantages (based on a qualitative or quantitative analysis) are shunned while those whose advantages outweigh their disadvantages are pursued.