How to calculate the counterclockwise torque? Using what formula? How to calculate the clockwise torque? Using what formula?
The Correct Answer and Explanation is:
To calculate torque, we need to use the following basic formula:τ=F×r×sin(θ)\tau = F \times r \times \sin(\theta)τ=F×r×sin(θ)
Where:
- τ\tauτ represents the torque.
- FFF is the force applied.
- rrr is the perpendicular distance from the axis of rotation to the point where the force is applied (also known as the lever arm).
- θ\thetaθ is the angle between the force vector and the lever arm.
Counterclockwise Torque:
Counterclockwise torque is generally considered positive in most cases. If a force is applied in such a way that it causes a rotation in the counterclockwise direction, the torque is positive. To calculate the counterclockwise torque:
- The angle θ\thetaθ will be less than 90 degrees for a typical force causing counterclockwise rotation.
- The torque will have a positive value.
Clockwise Torque:
Clockwise torque is typically considered negative because it results in a rotation in the opposite direction to counterclockwise motion. To calculate the clockwise torque:
- The force applied causes a clockwise rotation, which will make θ\thetaθ greater than 90 degrees.
- The torque will have a negative value, as per the convention.
For both counterclockwise and clockwise torque, the formula is the same; what changes is the direction of the applied force and the resulting direction of rotation. The key difference is in the sign convention, where counterclockwise torque is considered positive and clockwise torque is considered negative.
Example:
Suppose a force of 10 N is applied 3 meters away from a pivot point at an angle of 90 degrees (directly perpendicular). The torque would be:τ=10 N×3 m×sin(90∘)=30 Nm\tau = 10 \, N \times 3 \, m \times \sin(90^\circ) = 30 \, \text{Nm}τ=10N×3m×sin(90∘)=30Nm
If the force was applied in the opposite direction (clockwise), the torque would be negative:τ=−30 Nm\tau = -30 \, \text{Nm}τ=−30Nm
This negative sign indicates that the rotation is clockwise.
