How to Calculate Torque: Your Complete Guide

Examples of Torque Calculations

Here are a few examples that explain how to calculate torque.

Example 1: Perpendicular Force

Suppose you apply a force of 10 N at the end of a 0.5-meter wrench. The angle between the force and the lever arm is 90°.

Solution:

𝜏=𝑟×𝐹

𝜏=0.5 m×10 N

𝜏=5 Nm

Example 2: Tightening a Lug Nut

Imagine you're tightening a lug nut on a car tire with a wrench 0.5 meters long. You apply a force of 50 N at an angle of 30° to the handle. Find the torque applied to the lug nut?

Solution:

τ = 50 N × 0.5 m × sin(30°)

τ ≈ 12.5 N⋅m

Example 3: Seesaw Balance

Two children of different weights are playing on a seesaw. 

One child weighing 40 kg sits 2 meters from the fulcrum, while the other weighing 30 kg sits 3 meters away. To balance the seesaw, what distance from the fulcrum should the lighter child move to?

Solution:

We can set up a torque equation for each child:

• Child 1: τ₁ = 40 kg × 9.8 m/s² (gravity) × 2 m

• Child 2: τ₂ = 30 kg × 9.8 m/s² × 3 m (assuming constant gravity)

For the seesaw to balance, the torques must be equal (τ₁ = τ₂). Solve for the distance (d) the lighter child needs to move:

• d = (τ₁ × 3 m) / (30 kg × 9.8 m/s²) ≈ 2.65 m

Note: Don’t forget to convert units appropriately (e.g., weight to force) when applying the torque formula.

Example 4: Torque in a Car Engine

Imagine a scenario where you need to calculate the torque produced by a car engine. The engine applies a force to a crankshaft, which in turn causes rotation that ultimately powers the wheels of the vehicle. 

How can we calculate the torque produced by a car engine that applies a force of 1500 Newtons to a crankshaft, where the distance from the center of the crankshaft to the point where the force is applied is 0.1 meters? Assume the force is applied tangentially to the crankshaft.

Solution:

The torque formula is given by:

𝜏=𝑟×𝐹×sin(𝜃)

Since the angle 𝜃 is 90°, sin(90°)=1:

𝜏=0.1 m×1500 N×sin(90∘)

τ𝜏=0.1 m×1500 N×1

𝜏=150 Nm

Example 5:Rotational Torque in a Robotic Arm

Problem:

A robotic arm applies a force of 200 Newtons at the end of its 0.5-meter-long segment. The force is applied at an angle of 60 degrees to the arm. How can we calculate the torque produced by this force?

Solution:

The torque formula is:

𝜏=𝑟×𝐹×sin(𝜃))

Calculate sin(60∘), which is 3/2≈0.866

𝜏=0.5 m×200 N×sin(60∘)

𝜏=0.5 m×200 N×0.866

𝜏=100×0.866

τ=86.6Nm

Additional Considerations

• Torque as a Vector Quantity: While the formula illustrates how to find the magnitude of torque, torque is also a vector quantity with direction. The right-hand rule can be used to determine the direction of torque.

• Average Torque: In situations where the force or angle varies, you might need to calculate the average torque over time.

Practical Applications

Torque calculation is essential in various fields. Here are a few examples that show the importance of knowing how to calculate torque in Engineering Design:

• Automotive Engineering: Determining the torque output of engines.

• Structural Engineering: Ensuring stability in structures by calculating the torque on beams and supports.

• Mechanical Design: Designing and analyzing the performance of machinery and tools.

• Robotics: Ensuring precise and reliable movements.

Measuring Torque

Measuring torque is essential for ensuring the accuracy and reliability of various mechanical systems. 

This involves using tools like torque wrenches, which apply a specific torque to fasteners, and force-torque sensors, which measure the torque in both static and rotating systems such as engines and robotic arms. 

Accurate torque measurement helps in preventing mechanical failures, optimizing performance, and ensuring safety in applications ranging from automotive engines to robotic arms. Properly calibrated torque measurement tools are crucial for maintaining the integrity and efficiency of engineered systems.

Estimating Torque by Hand

In some practical situations, precise torque measurements might not be feasible. Estimating torque by hand involves applying known forces at known distances, using calibrated tools like torque wrenches to ensure accuracy.

Conclusion

By understanding the concept of torque and its formula, you can solve problems involving rotational motion and forces. 

This knowledge can be applied in various real-world scenarios, from simple tasks like tightening a screw to complex engineering applications. 

So, the next time you use a wrench or witness a machine in action, remember the invisible force of torque at play!