How do Newton’s laws of motion explain why it is important to keep the ice smooth on a hockey rink so that players can pass a puck as quickly as possible?

Smooth ice reduces the inertia of the hockey puck.
Smooth ice increases the force used to accelerate the hockey puck.
Smooth ice reduces the unbalanced forces that would slow the hockey puck.
Smooth ice decreases the reaction force that the ice exerts on the hockey puck.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)