In torque formula, what is the torque when the angle between radius and force is 90 degrees?

In torque formula, what is the torque when the angle between radius and force is 90 degrees?

• A. tau = r F
• B. tau = 0
• C. tau = r F sin 90
• D. tau = F / r

Answer: (C)

Torque measures how strongly a force tends to rotate an object around a pivot, and it depends on three things: how far the force is applied from the pivot (the lever arm), how big the force is, and how much of that force acts perpendicular to the lever arm. The standard expression for the magnitude is τ = r F sin θ, where θ is the angle between the radius (the lever arm) and the force. If the angle is 90 degrees, the force is perfectly perpendicular to the lever arm, so the full force contributes to rotation. Substituting 90 degrees gives τ = r F sin 90°, and since sin 90° = 1, this simplifies to τ = rF. Writing the torque as τ = r F sin 90° directly shows the angle dependence and, in this case, confirms the result rF. The value is maximum here because the force isn’t wasted on any component parallel to the lever arm. So the expression with sin 90° is the exact way to represent the torque for this situation, and it confirms that the torque equals rF when the angle is 90 degrees.

Torque measures how strongly a force tends to rotate an object around a pivot, and it depends on three things: how far the force is applied from the pivot (the lever arm), how big the force is, and how much of that force acts perpendicular to the lever arm. The standard expression for the magnitude is τ = r F sin θ, where θ is the angle between the radius (the lever arm) and the force.

If the angle is 90 degrees, the force is perfectly perpendicular to the lever arm, so the full force contributes to rotation. Substituting 90 degrees gives τ = r F sin 90°, and since sin 90° = 1, this simplifies to τ = rF. Writing the torque as τ = r F sin 90° directly shows the angle dependence and, in this case, confirms the result rF. The value is maximum here because the force isn’t wasted on any component parallel to the lever arm.

So the expression with sin 90° is the exact way to represent the torque for this situation, and it confirms that the torque equals rF when the angle is 90 degrees.