Question

A solid, 3.00-kg disk has a string wrapped around its circumference as shown below. The string is attached to the ceiling. When the disk is released, it accelerates downward as the string unrolls. The disk has a radius of 20.0 cm. What will be the linear velocity of its center of mass after it falls through a distance of 3.00 meters? (Note: not all the information given is needed.) Ignore friction.

  Ans: 6.26 m/s

Answer 1

by conservation of energy

initial energy = final energy

mgh = 0.5 * moment of inertia * angular velocity^2 + 0.5 * mv^2

mgh = 0.5 * 0.5 * m * r^2 * velocity^2 / r^2 + 0.5 * mv^2

gh = 0.5 * 0.5 * r^2 * velocity^2 / r^2 + 0.5 * v^2

9.8 * 3 = 0.5 * 0.5 * velocity^2 + 0.5 * v^2

velocity = 6.26 m/s