# Why do r and F need to be perpendicular for two angles to give the same torque?

• Ronnin
In summary, if r and F are not perpendicular, there will always be two angles between their directions that will result in the same torque, as determined by the definition of torque. This is due to the fact that the magnitude of the torque is determined by the sine of the angle between the position vector and the force vector, and since the sine function is symmetrical, the same torque will be produced at angles theta and pi-theta. However, this only applies to the magnitude of the torque, as the actual angle between the two directions will change.
Ronnin
Unless r and F are perpendicular, there are always two angles between their directions that give the same torque for given magnitudes of r and F. Explain why?

Perhaps I cannot visualize the question, but I cannot see how this can be. As the force moves to the perpendicular position the torque increases. Am I missing something?

Use the definition of torque. If one angle between the p.v and force vector is theta, what about the other?

Edit: I guess this holds only for the magnitude of the torque.

Last edited:
$$\tau = rF \sin \theta$$

$$sin \theta = \sin (\pi - \theta)$$​

I guess I figured that would put the angle outside of between the two angles.

## 1. What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance between the force and the axis of rotation.

## 2. What is the difference between r and F in torque?

r represents the distance between the applied force and the axis of rotation, while F represents the magnitude of the applied force. These two values are multiplied together to calculate the torque.

## 3. How do you calculate torque using two angles?

To calculate torque using two angles, you would use the formula T=rFsinθ, where r is the distance between the force and the axis of rotation, F is the magnitude of the force, and θ is the angle between the force vector and the lever arm.

## 4. What is the unit of measurement for torque?

The unit of measurement for torque is Newton meters (N*m) in the International System of Units (SI). In the English system, it is measured in foot-pounds (ft-lb) or inch-pounds (in-lb).

## 5. How does torque affect rotational motion?

Torque is responsible for causing rotational motion in an object. The greater the torque applied, the greater the rotational acceleration will be. If the torque is applied in the same direction as the rotation, it will cause the object to speed up. If the torque is applied in the opposite direction, it will cause the object to slow down or stop.

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