Net Torque & Sign of Torque - Online Tutor, Practice Problems & Exam Prep

When multiple forces act on an object, they produce torques that can be clockwise (negative) or counterclockwise (positive). The net torque is the sum of individual torques, calculated using the equation τ = Frsin(θ). Unlike forces, which are vectors, torques are scalars with orientation. If the net torque equals zero, the object is in rotational equilibrium, indicating no net rotation. Understanding these concepts is crucial for analyzing rotational dynamics effectively.

Net Torque & Sign of Torque

Hey, guys. So in this video, we're going to talk about what happens when you have multiple forces producing multiple torques on the same object. In other words, trying to get the object to spin in different directions. Let's check it out. The first thing we need to talk about is the sign of torque. You might remember that with different forces, if you have a force going in different directions like the positive x-axis, the negative x-axis, we use signs to indicate direction. The same thing happens with torques, but the direction depends on which way you're trying to spin something. So, if you're trying to spin something in the clockwise direction, which is the direction of the clock, it's negative, and counterclockwise is positive.

There are two ways that you can remember this. The reason counterclockwise is positive is because it follows the unit circle, it starts at 0 degrees and grows in that direction. Another way you can think about this is that the direction of the clock is backwards, which means 'clock is backwards.' These are two ways that you can remember the direction. This is a standard direction for rotation, so you should remember that. Now, what happens if you have multiple torques? We can calculate the net torque, which is the resultant torque. It's one torque that represents a combination of all of them. And the net torque is simply the addition of the individual torques. So if you have two torques, it would look like simply torque 1 plus torque 2.

The big difference between forces and torques is that forces are vectors, they have a direction, a theta, and can point in different directions. A torque, however, is a result of a force and is a twist that's either clockwise or counterclockwise, not really a direction in the same way that a force can point at an infinite number of angles. It's just really 2 options. This means torques are scalars, not vectors. They have an orientation that could be either positive or negative. So, we're going to use simple additions and not vector additions to find torque. Remember, for forces, if you push this way with a force of 3 and this way with a force of 4, the net force is not 7. The net force is 5 because this is vector addition. With torques, if you have a torque of 3 and a torque of 4, the answer is always 7 because it's simple addition, not vector addition. Forces are vectors, but torques are scalar.

Let's do a quick example here. So I have two forces acting on the same door. The door is 3 meters long. It says force 1 acts on the center of the door. So this is the middle right here. So I'm going to say that this is 1.5 half of the length, and this is 1.5 the other half of the length. It says f 2 is directed at 30 degrees above the x-axis, so it looks like this. We want to know what is the net torque and we also want to use signs, positive or negative, to indicate whether they're clockwise or counterclockwise, the direction, the orientation of the torques.

The definition of a torque is fr sin(θ). So it's going to be fr1 sin(θ1) and fr2 sin(θ2). We need to draw the r vector for each one of these guys, figuring out the theta, and then plugging them into the torque equation. Following these steps, we determine that torque 1 is negative, and torque 2 is positive because of their respective counterclockwise and clockwise orientations. So, we have t1 negative and t2 positive. This results in a net torque of zero, indicating rotational equilibrium: no spin occurs.

That's it for this one. Cool. Let me know if you have any questions and let's keep going.

A 2-m long bar is free to rotate about an axis located 0.7 m from one of its ends. Two forces act on the bar, F₁ = 100 N and F₂ = 200 N, and both make 30° with the bar. Find the Net Torque on the bar. Use +/− to indicate direction.

• A. −95 N•m
• B. +95 N•m
• C. −165 N•m
• D. +165 N•m

Here’s what students ask on this topic:

What is the difference between net torque and individual torque?

Net torque is the sum of all individual torques acting on an object. Individual torque is produced by a single force and is calculated using the equation $\tau =Fr\sin \left(\theta \right)$. Net torque considers the direction of each torque, where clockwise torques are negative and counterclockwise torques are positive. If the net torque is zero, the object is in rotational equilibrium, meaning it does not rotate.

How do you determine the sign of torque?

The sign of torque depends on the direction of rotation it causes. If the torque causes a clockwise rotation, it is considered negative. If it causes a counterclockwise rotation, it is considered positive. This convention aligns with the unit circle, where counterclockwise is positive. Remembering that the direction of a clock is backward can also help in determining the sign.

What is the equation for calculating torque?

The equation for calculating torque is $\tau =Fr\sin \left(\theta \right)$, where $\tau$ is the torque, $F$ is the force applied, $r$ is the distance from the axis of rotation to the point where the force is applied, and $\theta$ is the angle between the force vector and the lever arm.

What happens when the net torque on an object is zero?

When the net torque on an object is zero, the object is in rotational equilibrium. This means that all the individual torques cancel each other out, resulting in no net rotation. The object will either remain stationary or continue rotating at a constant angular velocity if it was already in motion.

Why are torques considered scalars and not vectors?

Torques are considered scalars because they do not have a direction in the same sense as vectors. Instead, they have an orientation: clockwise (negative) or counterclockwise (positive). Unlike forces, which can point in an infinite number of directions, torques only have two possible orientations, making them scalars with a sign indicating their rotational direction.