Net Torque & Sign of Torque: Videos & Practice Problems

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

When analyzing the effects of multiple forces on an object, it's essential to understand how these forces produce torques that can cause the object to spin in different directions. The direction of torque is indicated by its sign: clockwise torque is considered negative, while counterclockwise torque is positive. This convention aligns with the unit circle, where angles increase in the counterclockwise direction starting from the positive x-axis.

To find the net torque acting on an object, you simply add the individual torques together. Unlike forces, which are vector quantities and require vector addition, torques are scalar quantities. This means that when calculating net torque, you can use straightforward addition. For example, if you have two torques, τ₁ and τ₂, the net torque (τ_net) is given by:

$$\tau_{net} = \tau_1 + \tau_2$$

In a practical scenario, consider a door subjected to two forces. The torque produced by each force can be calculated using the formula:

$$\tau = F \cdot r \cdot \sin(\theta)$$

where \(F\) is the force applied, \(r\) is the distance from the pivot point to the point of force application, and \(\theta\) is the angle between the force vector and the lever arm. The orientation of the torque (positive or negative) is determined by the direction of the force relative to the pivot point.

For instance, if a force is applied at the center of a 3-meter door, and another force is applied at an angle of 30 degrees above the x-axis, you would first identify the distances \(r_1\) and \(r_2\) for each force. The torque for each force can then be calculated, taking care to assign the correct sign based on the direction of rotation each force induces.

After calculating the individual torques, you can sum them up. If the result is zero, it indicates that the torques are balanced, leading to a state of rotational equilibrium where the object does not spin. This concept is crucial in understanding how forces interact in a system and the conditions necessary for maintaining stability.

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

Answer: (D)

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.