# How does a spinning disk respond to an impulse? [closed]

The figure shows a disk spinning with an angular velocity $$\omega_z$$. The disk is suspended from a long string.

I would like to know the following:

• How does the disk respond to an impulse $$J$$?
• What are the differential equations that describe this response?

Let us assume that hitting the disc doesn't cause any loss of energy due to friction. We can conserve angular momentum about the center: $$JR=I_x\omega_x$$ where $$I_x=mR^2/4$$ So our disc can be thought of as independently rotating about $$z$$ and $$x$$ axes. We can find the component of $$\omega_x,\omega_z$$ to get $$\omega_{net}$$ along which will be actual axes of rotation of our disc.