Question

At which angle torque is zero?

Answer 1

Torque is zero when the angle between the force and the lever arm is
`0^(\circ)` or
`180^(\circ)`.

Step-by-step explanation:

Assume that the force in this question is applied on a lever. Let
`\theta` denote the angle between the force and the lever arm, and let
`r` denote the length of the lever arm.

The equation for the torque
`\tau` that this force
`F` exerts on the lever would be
`\tau = F\, r\, \sin(\theta)`.

If
`0 \le \theta \le 180^(\circ)`,
`\sin(\theta) = 0` either when
`\theta = 0^(\circ)` or
`\theta = 180^(\circ)`.

Therefore, as long as neither the force
`F` nor the distance
`r` is zero, torque would be zero only if the angle
`\theta` is either
`0^(\circ)` or
`180^(\circ)`.

Refer to the diagram attached. In torque calculations in general,
`\theta` is the angle between:

• the force, and
• the line joining the axis of rotation and the point where the force is applied.

In the general case
`r` would measure the distance between this point and the axis of rotation.

Likewise, using the equation
`\tau = F\, r\, \sin(\theta)`, torque would be zero when the angle
`\theta` is either
`0^(\circ)` or
`180^(\circ)`.