Write down the equation to calculate the torque if the magnitude of a force and the lever arm are given.
The correct answer and explanation is :
Torque Equation
The equation to calculate torque ((\tau)) when the magnitude of the force ((F)) and the lever arm ((r)) are given is:
[
\tau = r \times F \times \sin(\theta)
]
where:
- (\tau) = Torque (measured in Newton-meters, Nm)
- (r) = Lever arm (distance from the pivot point to the point where the force is applied, measured in meters)
- (F) = Force applied (measured in Newtons, N)
- (\theta) = Angle between the force vector and the lever arm
Explanation (300 words)
Torque is a measure of the rotational force applied to an object around a pivot point. It determines how effectively a force can cause an object to rotate. The greater the torque, the greater the tendency of an object to rotate.
The equation (\tau = r \times F \times \sin(\theta)) incorporates three key factors:
- Lever Arm ((r)) – The distance from the pivot point to the point where force is applied. A longer lever arm increases torque, making it easier to rotate an object.
- Force ((F)) – The magnitude of the applied force. A larger force generates a greater torque.
- Angle ((\theta)) – The effectiveness of the force depends on its direction. The torque is maximum when the force is applied perpendicular to the lever arm ((\theta = 90^\circ), where (\sin(90^\circ) = 1)). If the force is applied parallel ((\theta = 0^\circ)), no torque is produced ((\sin(0^\circ) = 0)).
In practical applications, torque is crucial in machines, engines, and tools like wrenches. For example, when using a wrench to tighten a bolt, increasing the length of the wrench handle (lever arm) or applying more force increases the torque, making it easier to turn the bolt.