Unit 5.8 – Torque

• Turning a door handle requires applying torque to rotate the handle around its pivot point.
• Tightening a bolt with a wrench involves applying torque to rotate the bolt.

Key Points About Torque

1. Definition:
   • Torque ($𝜏$) is the product of the force applied and the perpendicular distance from the pivot point to the line of action of the force.
   • Formula:
     $$𝜏=𝐹\cdot 𝑟\cdot \sin 𝜃$$
     Where:
     • $𝜏$: Torque ($\text{N}\text{cdotp}\text{m}$)
     • $𝐹$: Force applied ($\text{N}$)
     • $𝑟$: Distance from the pivot point to the point where the force is applied ($\text{m}$)
     • $𝜃$: Angle between the force vector and the line connecting the pivot to the point of application
2. Units of Torque:
   • The SI unit of torque is the Newton-meter ($\text{N}\text{cdotp}\text{m}$).
3. Direction of Torque:
   • Torque can cause clockwise or counterclockwise rotation.
   • By convention:
     • Counterclockwise torque is positive.
     • Clockwise torque is negative.
4. Factors Affecting Torque:
   • Force: Greater force increases torque.
   • Distance ($𝑟$): Greater distance from the pivot increases torque.
   • Angle ($𝜃$): Torque is maximum when the force is applied perpendicular to the lever arm ($𝜃={90}^{\circ }$).

Detailed Notes with Bullets

1. Why Do We Need Torque?

• Torque explains how forces cause rotation in everyday objects.
• Example: Opening a door requires applying torque to rotate it around its hinges.

2. How Does Torque Work?

• Torque depends on three factors:
  • Magnitude of Force ($𝐹$): Larger forces produce greater torque.
  • Lever Arm ($𝑟$): Applying force farther from the pivot increases torque.
  • Angle ($𝜃$): Torque is greatest when the force is applied perpendicular to the lever arm.

3. Special Cases of Torque

• When $𝜃={90}^{\circ }$:
  • $\sin {90}^{\circ }=1$, so $𝜏=𝐹\cdot 𝑟$.
  • Example: Pushing a door at a right angle to the handle maximizes torque.
• When $𝜃=0^{\circ }$:
  • $\sin 0^{\circ }=0$, so $𝜏=0$.
  • Example: Pushing directly toward the hinge of a door produces no torque.

4. Real-Life Examples of Torque

• Opening a Door:
  • The farther you push from the hinge, the easier it is to open the door because torque increases with distance.
• Tightening a Bolt:
  • Using a longer wrench increases the torque, making it easier to tighten or loosen the bolt.
• Seesaw:
  • A heavier person sitting closer to the pivot can balance a lighter person sitting farther away due to equal torques.

Quick Review, Exam Tips, Tricks & Traps

Key Points to Remember

• Torque is the rotational effect of a force and depends on the force, distance, and angle.
• Use the formula:
  $$𝜏=𝐹\cdot 𝑟\cdot \sin 𝜃$$
• Torque is maximum when the force is applied perpendicular to the lever arm ($𝜃={90}^{\circ }$).

Exam Tips

1. Always check if the question provides the force ($𝐹$), distance ($𝑟$), and angle ($𝜃$).
2. Convert units carefully:
   • Force should be in Newtons ($\text{N}$).
   • Distance should be in meters ($\text{m}$).
3. Pay attention to the direction of torque (clockwise or counterclockwise).

Common Traps

1. Students often forget to include the sine term ($\sin 𝜃$) in calculations unless the force is perpendicular to the lever arm.
2. Misinterpreting the role of distance: Torque decreases if the force is applied closer to the pivot.

Tricks for Competitive Exams

1. Look for keywords like "rotation," "pivot," or "lever arm" to identify torque problems.
2. In MCQs, eliminate options where torque decreases with increasing distance—it’s impossible unless the force changes.
3. Use proportional reasoning:
   • If the force doubles, torque doubles.
   • If the distance doubles, torque doubles.

Quick Recall Table

Additional Content: Real-Life Examples and Applications

1. Everyday Tools

• Wrenches: Longer wrenches increase the torque, making it easier to tighten or loosen bolts.
• Screwdrivers: Applying force at a right angle to the handle maximizes torque for turning screws.

2. Seesaws and Balances

• Torque explains how seesaws work:
  • Equal torques balance the seesaw.
  • A heavier person can balance a lighter person by sitting closer to the pivot.

3. Rotating Machinery

• Motors and engines use torque to generate rotational motion.
• Example: The torque produced by a car engine determines its ability to accelerate.

4. Sports and Activities

• Torque is involved in activities like swinging a bat, throwing a ball, or pedaling a bicycle.
• Example: Cyclists apply torque to the pedals to rotate the wheels.