Torque: Definitions and Concepts

• Torque (τ)

  • Definition: Torque is the rotational equivalent of force.

  • Units: Measured in newton-meters (N ⋅ m).

QuickCheck Examples

• QuickCheck 7.10

  • Scenario: Four forces are applied with equal strength to open a door.

  • Options:

  • A. Force F1

  • B. Force F2

  • C. Force F3

  • D. Force F4

  • E. Either F1 or F3

  • Conclusion: The most effective force for opening the door is F1 because it exerts the largest torque about the hinge.

Torque Direction

• Direction of Torque

  • Positive Torque: Rotates the object in a counter-clockwise direction.

  • Negative Torque: Rotates the object in a clockwise direction.

Net Torque

• Net Torque

  • Definition: The sum of the torques due to the applied forces.

  • Importance: Used to determine rotational motion balance in a system.

Static Equilibrium

• Definition of Static Equilibrium

  • An object at rest achieves static equilibrium when:

  • The net force on the particle is zero.

  • For extended objects, both net force and net torque must be considered:

  • Condition for Extended Objects:

    • When the net force and the net torque are both zero, the object is in static equilibrium.

    • If the net force is zero but the net torque is not zero, static equilibrium is not achieved.

Conditions for Static Equilibrium in Extended Objects

• Two Conditions

  • Condition 1: The net force on the object must be zero.

  • Condition 2: The net torque on the object must be zero.

Choosing the Pivot Point

• Choosing Pivot Point for Calculating Torque

  • Concept: For an object in static equilibrium, the net torque about any point must be zero.

  • Flexibility: You can choose any point as the pivot point to calculate torque.

QuickCheck 8.2 Example

• Scenario: A scale placed halfway along a rod.

• Options for Scale Reading:

  • A. 500 N

  • B. 1000 N

  • C. 2000 N

  • D. 4000 N

• Important Note: Answering this requires reasoning rather than calculation.

Real-World Applications and Examples

Example Exercises

• Example 1:

  • A ball hangs from a 4 m, 300 N beam.

  • Questions:

  • What is the tension in the cable?

  • What is the force on the hinge where the beam meets the wall?

• Example 2:

  • A 3.0 m long ladder leans against a frictionless wall at a 60° angle.

  • Question: What is the minimum value of μs, the coefficient of static friction with the ground, that prevents the ladder from slipping?

Stability and Balance

• Definition of Stability in Extended Objects

  • An extended object is stable when its center of gravity remains over its base of support.

  • When in static equilibrium, if the center of gravity is maintained over the base of support, the object returns to its stable position if disturbed.

• Example of Stability:

  • Scenario: A cat on a plank.

  • Explanation:

  • When the cat is at the left end, the system is stable (center of gravity is aligned).

  • As the cat moves right, a tipping point is reached when the center of gravity aligns with the edge of the table, leading to instability and tilting.

Laboratory Problems

• Problem Lab: Mass of a Meterstick

  • Purpose: Determine the mass of a meterstick through analysis.

  • Procedure:

  • Labeled diagram and calculations required to find the mass.

  • Compare measured mass to calculated value.

  • Considerations: Discuss potential sources of error and physical reasons for discrepancies.