A ball with mass 0.200kg on a string is being rotated around with an angular velocity of 12.0 rad/s at a radius of 12.5cm. The radius is suddenly decreased to 7.25 cm. What is the new angular velocity? (hint: the moment of inertia for a particle in rotation about a center point is I = mr^2)

Question

A ball with mass 0.200kg on a string is being rotated around with an angular velocity of 12.0 rad/s at a radius of 12.5cm. The radius is suddenly decreased to 7.25 cm. What is the new angular velocity?  (hint: the moment of inertia for a particle in rotation about a center point is I = mr^2)

amistre64 · Answer

theres a conversation of something in this type of system ... can you remember what it was?

amistre64 · Answer

angular momentum of an isolated system is conserved

amistre64 · Answer

$$L\cong I\omega$$
You are given I and omega; so it should be the same for before and after the string is shortened

amistre64 · Answer

$$m~r_1^2~\omega_1=m~r_2^2~\omega_2$$
$$\frac{m~r_1^2~\omega_1}{m~r_2^2}=~\omega_2$$
$$\left(\frac{r_1}{r_2}\right)^2\omega_1=~\omega_2$$