The Direction of Each Torque
When a force is applied to a beam in a direction that does not extend through the axis of rotation (i.e., the fulcrum), a torque is said to exist. A torque in and of itself will cause the beam to rotate about its fulcrum. The direction that it rotates can be described as counter-clockwise or clockwise. This direction of rotation can be determined by the direction of the force and the side of the fulcrum upon which it is exerted. In the event that it is not obvious, an upward force applied on the right side of the fulcrum or a downward force applied to the left side of the fulcrum will cause a counter-clockwise rotation. On the other hand, a downward force applied on the right side of the fulcrum or an upward force applied to the left side of the fulcrum will cause a clockwise rotation. A torque is typically assigned a positive or a negative sign based on the direction of rotation that it causes. A torque that causes a counter-clockwise rotation is a positive torque. On the other hand, a torque that causes a clockwise rotation is a negative torque. You will need to determine the direction (expressed with a + or - sign) of the individual torques caused by the three given forces.
The Magnitude of Each Torque
The magnitude of each torque can be determined by multiplying the force by the so-called moment arm. When the force is perpendicular to the beam (as it is here), you can calculate the torque by simply multiplying the given force value by the distance between the point at which the force is applied to the fulcrum at the center of the beam. Vertical hash marks are displayed on the beam and each force is applied at the location of one of the hash marks. And while a distance scale is not given and a distance unit is not stated, you can simply assign each hash mark as being "1 distance unit" from the previous hash mark. This allows you to measure a distance from the point of application of each force to the fulcrum. Once you measure this distance, you can use it to calculate the torque (Force * distance). You will need to calculate the magnitude of the torques caused by the three given forces. Include a + or - sign for each torque using the information from the previous section (The Direction of Each Torque).
To Balance or Not to Balance?
The individual torques on the beam will balance each other if the sum of all the clockwise torques is equal to the sum of all the counter-clockwise torques. When this balance is established, the net torque (Στ) is 0 and the beam remains stationary. On the other hand, if the sum of all the clockwise torques is NOT equal to the sum of all the counter-clockwise torques, there will be a net torque (an unbalanced torque) and an angular acceleration.
So to answer the two questions, add all the negative torques; then add all the positive torques. How do the two sums compare? Use the rule in the previous paragraph to answer the two questions.
