Torque exercise problem

Question

I am learning physics with help of this site https://www.khanacademy.org/

And I have stumbled upon a task that I can not completely understand

The task says: A gasoline engine producing Nm of torque at a rotational speed of 300 rad/s is used to drive a winch and lift a weight as shown in figure 6. The winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear. What mass could be raised with this setup? (Assume the winch is in rotational equilibrium, i.e. the mass is traveling up at constant velocity).

They solved it by equalising torque of winch (weight) with a torque of machine and dividing torque of machine with reduction in speed (tao(winch)=tao(machine)/R.

My question is why does tao (winch) = tao (engine)/R and why does reduction in speed result in bigger tao (winch).

Is the reduction in speed resulted in bigger tao (winch) because the weight has caused the reduction in speed?

link to a task - https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/a/torque

Answer 1

You can do an analog with forces and velocity. If the power $P$ of a machine is fixed, according to $P=F\cdot v$, the slower the speed, the stronger the force. It is similar with torques and angular velocities.