Find the torque on the meter stick for each situation. Ignore the mass of the meter stick. At 1/2 meter there is a 1000g weight. At 1 meter on the same stick there is a 500g weight. What is the torque? Not understanding how to come up with this answer. Keep getting it wrong.

Torque about what point? One end? The center?

I don't understand your question, however here are other parts of the same question and the answers are correct.

All on the same 1 meter stick. Assuming g=10m/s/s:
500g weight on the right end of the stick; torque = 5 Nm.
750g weight on the right end of the stick; torque = 7.5 Nm
500g weight at the 1/2 way point on the stick; torque = 2.5 Nm.

Ok, that is measureing torque about the free end.

So on your,
Torque=force*distance+force*distance
Torque=1kg*10N/kg*.5m + .5kg*10N/kg*1m
= 5Nm+5Nm=10Nm

Now note: 10m/s^2=10N/kg, which is easier to use in these, you are looking for force*distance

Thanks much. This is what I needed to understand.

angular momentum of a system of particles

To find the torque on the meter stick in each situation, you need to understand the concept of torque and how to calculate it. Torque is the rotational equivalent of force and is defined as the product of the force applied and the lever arm distance.

In this case, the force is the weight of the objects (1000g and 500g weights), and the lever arm distance is the perpendicular distance between the pivot point and the line of action of the force. The pivot point in this case is assumed to be at the end of the meter stick.

To calculate the torque, you can use the equation:

Torque = Force × Perpendicular distance

Let's calculate the torque at ½ meter and at 1 meter on the meter stick:

1. Torque at ½ meter:
Force = 1000g (weight) = 1000g × 9.8 m/s^2 (acceleration due to gravity)
= 9.8 N (convert grams to Newtons)
Perpendicular distance = 0.5 meters

Torque at ½ meter = 9.8 N × 0.5 meters = 4.9 Nm (Newton-meters)

2. Torque at 1 meter:
Force = 500g (weight) = 500g × 9.8 m/s^2
= 4.9 N
Perpendicular distance = 1 meter

Torque at 1 meter = 4.9 N × 1 meter = 4.9 Nm

So, the torque on the meter stick at ½ meter is 4.9 Nm, and at 1 meter is also 4.9 Nm.