How To Calculate Rotational Torque

Rotational Torque Formula:

\[ \tau = r \times F \times \sin(\theta) \]

Torque (τ):

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1. What Is Rotational Torque?

Rotational torque is a measure of the force that can cause an object to rotate about an axis. It is a vector quantity that depends on the magnitude of the force, the distance from the axis, and the angle between the force vector and the lever arm.

2. How Does The Calculator Work?

The calculator uses the torque formula:

\[ \tau = r \times F \times \sin(\theta) \]

Where:

\( \tau \) — Torque (N·m)
\( r \) — Radius or lever arm length (m)
\( F \) — Applied force (N)
\( \theta \) — Angle between force vector and lever arm (degrees)

Explanation: The formula calculates the rotational effect of a force applied at a distance from a pivot point, with the sine function accounting for the angular component of the force.

3. Importance Of Torque Calculation

Details: Torque calculation is essential in mechanical engineering, physics, and various applications including automotive systems, machinery design, and structural analysis to ensure proper rotational motion and mechanical advantage.

4. Using The Calculator

Tips: Enter radius in meters, force in newtons, and angle in degrees. All values must be valid (radius > 0, force > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between torque and force?
A: Force causes linear acceleration, while torque causes rotational acceleration. Torque depends on both the magnitude of force and its point of application relative to the axis.

Q2: What happens when the angle is 90 degrees?
A: At 90 degrees, sin(θ) = 1, so torque is maximized (τ = r × F). This is when the force is applied perpendicular to the lever arm.

Q3: What is the unit of torque?
A: The SI unit is newton-meter (N·m). In imperial systems, it's often measured in pound-feet (lb·ft).

Q4: Can torque be negative?
A: Yes, torque can be negative indicating rotation in the opposite direction (clockwise vs counterclockwise).

Q5: How does torque relate to angular acceleration?
A: According to Newton's second law for rotation: τ = I × α, where I is moment of inertia and α is angular acceleration.