You might want to look at accelerometers or possible tilt sensors for detecting any movement. I don't have much experience with accelerometers but I do with tilt sensors. Some can be had with a sensitivity range of 0-0.5 degrees with a 4-20mA output so you could trigger the motor from this signal. However, I have not seen any that derive power from 120VAC although I am sure they are available. Otherwise, you may have to build a DC supply from the 120 to run the sensor. Their may be some other technologies to look at but none come to mind right now.
The load you need to switch is too large for the sensor to switch directly (depends on the sensor you select). In any case, since you are running a motor with this then a contactor/starter should be used (overload protection is required so get a starter (contactor with overloads)) with a 120VAC coil. If the coil is 120 then you can use the same power that feeds your motor to run your controls (sensor and starter). As far as turning the motor on with a switch when the sensor is off, you could just use a properly rated switch (120VAC with current rating equivalent to the starter coil current) in parallel with the rest of the controls. Granted a 4-20mA signal is not adequate to pull in the starter so if 4-20mA is used some other circuitry will have to be made.

Thanks for the help. I found a sensor ubs010100 that is a sensor which is about 1/4" x 1/4" x 1/2".But it to is only 4-20 ma. I am reconsider the load, I may use your ideal for the motor and use the other to control the light(with motion sensor and dpdt contacts) If the total load on the lights is only 7 lights at 75w. each, could I use then 4-20ma(sensor and dpdt) to control just the lights?

I am not sure I understand everything your tryig to do. When would the lights be turned on? When the motor is on?

To answer your last question; I would say the 4-20mA would not drive your lights directly. Perhaps you mean the 4-20mA would pull-in a relay that would in turn energize your lights and/or motor. You could play with the 'pull-in' voltage rating of the relay you select to coordinate with the output of the sensor. You need to check on the maximum load of the 4-20mA sensor to make sure it has enough voltage to supply the load with 20mA. Most 4-20mA equipment the max load is around 500 ohms. So if the sensor is supplied with say 12VDC and you want to send 20mA into a load the maximum load will be 12/.02=600 ohms or less.   

I have the motor problem reslove, thank to your suggestion. Now the second part of the project is to have a sensor to  turn on 6-60w lights with a standard wall switch. The same requirement exist with the size restrictions,it must work as a standard switch except when movement is detected, the contacts will pull in,and when the switch is switched on then off, the contact would be released and the light would work of the switch.Do you think I could use a mercury switch for the amount of amps? I dont think I would be restricted to 4-20ma like I am with the other sensor.(If I used the mercury switch)  

Make sure the switch is rated for the wattage.
I am not that familiar with mercury switch operation but I assume this is what is giving you the movement indication. If you review the data sheet for the one selected it will quickly let you know if it is rated for that kind of current. If it is not, just use a relay. The sensor would energize the relay and the relay would turn on the lights. You might also choose to have the standard switch energize the coil of the relay as well.