Problem Statement:

A spur gear train consists of three gears connected in series: Gear A$,$ Gear B$,$ and Gear C$.$ The specifications are as follows:

Gear $A$ : Driver gear with $20$ teeth, rotating at $600$ rpm clockwise.

Gear B: Intermediate gear with $40$ teeth, mounted on the same shaft as Gear C $.$

Gear $C$ : Output gear with $60$ teeth.

Assume the gears are connected correctly without slippage, and the direction of rotation alternates between gears.

Questions:

What is the speed of Gear B in rpm$?$

What is the speed of Gear C in rpm $?$

Determine the overall gear ratio of the train $($from Gear A to Gear C$).$

If Gear A transmits a torque of $50$ Nm $,$ calculate the torque transmitted to Gear C $($ignore losses due to friction$).$

What is the direction of rotation of Gear C relative to Gear A$?$