A hand-powered laboratory centrifuge, used in remote field clinics to separate blood plasma samples, contains a rotor assembly driven by a gear system as shown in the diagram.
The system works as follows:
- Handle A is attached to the larger gear B, which rotates about a fixed axle.
- Gear B meshes with a smaller gear C, which is attached directly to the spindle of the centrifuge rotor.
- Gear C rotates at a much higher angular speed than gear B.
A tangential force of 12 N12\text{ N}12 N is applied to the crank handle A. Handle A is located at a radial distance of 75 mm75\text{ mm}75 mm from its center of rotation.
Calculate the input torque on gear B.
Gear C rotates exactly eight times for every one revolution of gear B. Deduce whether it is possible for the torque on gear C to be greater than one-eighth of the input torque.
It takes 2.5 s2.5\text{ s}2.5 s for the centrifuge rotor to accelerate from rest to an operating angular speed of 60 rad s−160\text{ rad s}^{-1}60 rad s−1. The torque acting on gear C is constant and equal to 0.048 N m0.048\text{ N m}0.048 N m during this acceleration. Assuming frictional resistance is negligible, calculate the moment of inertia of the rotor assembly about its axis of rotation.
The gears are made of nylon (a polymer). Explain, with reference to angular impulse, why a large force is exerted on the gear teeth if the user attempts to stop the spinning rotor too quickly by holding the handle.