I think that is an induction motor from a washing machine. 180W is the rated output power (mechanical power). 1600 rpm is the rated speed. So that means that when you power it from 120V at 60Hz, it will deliver 180W when it is spinning at 1600 RPM. This also implies that the synchronous speed of the motor is 1800 rpm. Conceptually, synchronous speed is the speed at which the torque is zero. As you load the motor, the motor slows down (this is called slip) and the torque increases linearly with slip.
So 1800-1600 = 200 rpm. That 200 rpm is the slip required for the motor to put out its rated power and torque. Let's calculate torque.
Power = speed * torque
If we use rad/sec and N-m, power will be in Watts. So let's convert. 1600 rpm = 26.7 rev/sec. 26.7 * 2pi = 168 rad/sec.
If Power = speed * torque, then torque = power/speed. So 180W / 168 rad/sec = 1.07 N-m at rated power. So now we know that when slip = 200 rpm, torque will be 1.07 Newton meters. Likewise, if slip = 100 rpm, then torque must be 0.5035 Newton meters.
So in general, torque is as follows:
T = 1.07 * (slip / 200)
It will be in Newton meters. Slip is in rpm. You calculate slip as follows: 1800 - rpm, where "rpm" is the actual rpm.
So, breaking it all down, measure the actual no-load rpm. Take 1800 rpm, and subtract the actual no-load rpm. This is the no-load slip.
Divide by 200, and multiply by 1.07. Now you have the no-load torque. Approximately. You can also calculate the no load output power, since all you need is torque and speed (just multiply rad/sec * Newton-meters to get power in Watts).