Definition of Torque

  • Torque is defined as the rotational force that contributes to the change in rotational motion of an object.

  • It is responsible for the rotational acceleration of an object.

Factors Determining Torque

  • Magnitude of Force (F): The strength of the force applied.

  • Distance (r): The perpendicular distance from the pivot point (or axis of rotation) to the line of action of the force.

  • Angle (theta): The angle at which the force is applied relative to the radius vector from the pivot point to the point of force application.

Examples of Torque

Example 1: Pirate Wheel

  • Two pirates are pulling on a ship's steering wheel from different sides:

    • Force from Pirate 1 (F1): 72 N at 50 degrees from the horizontal.

    • Force from Pirate 2 (F2): 58 N at 90 degrees

  • Calculating Net Torque:

    • Torque from Pirate 1 can be calculated as:
      Torque 1 = Force 1 times Distance times sin(Theta 1) where Theta 1 = 50 degrees.

    • Torque 1 = 72 N times 0.74 m times sin(50 degrees)

    • Torque from Pirate 2 is:
      Torque 2 = Force 2 times Distance times sin(90 degrees) = 58 N times 0.74 m times sin(90 degrees)

    • Resulting net torque affecting the motion of the wheel:
      Net Torque = Torque 1 - Torque 2 = 41 Nm - 58 Nm = -2 Nm

    • Indicating a net torque of +43 Nm clockwise (cw) means Pirate 2 wins.

Example 2: Pulley

  • A pulley system with:

    • Radius R, mass m, and rotational inertia I is used.

  • Tension in the string attached to two blocks is measured as:
    Tension 1 and Tension 2, where Tension 2 > Tension 1.

  • The net torque exerted by the two tensions on the pulley is:
    Net Torque = Tension 1 times Radius - Tension 2 times Radius

Example 3: Torque Exerted by a Hanging Block

  • Analyzing the torque on a disk when a mass m0 hangs from a string wrapped around it.

  • Questions posed about whether the torque equals m0 times g times R0 when it begins to move:

    1. No, because the string's tension is less than the block’s weight.

    2. If it were equal, the block would not accelerate downwards.

Torque Problems

Problem 1: Net Torque on Fixed Wheels

  • A system of two wheels with four external tangential forces is assessed.

  • The objective is to determine the magnitude of the net torque about the rotational axis of the wheels.

Problem 2: Static Equilibrium of See-Saws

  • Examination of three see-saws in equilibrium:

    • Ensuring that all torques are balanced, maintaining a state of rest.

    • Students calculate missing variables needed to show balanced torque conditions.

Problem 3: Net Torque Calculation in See-Saws

  • Calculating net torque for different masses placed on a see-saw at varied distances.

  • Scenarios include:

    • Option a: Naomi, mass (1/2 m), at distance r.
      Torque = (1/2) times m times g times r

    • Option b: Carlos, mass (3/2 m), at distance (3/2 r).
      Torque = (3/2) times m times g times r

    • Option c: Peng, mass 2m, at distance (1/2 r).
      Torque = 2 times m times (1/2) times g times r = m times g times r

Problem 4: Torque on a Pulley from Tension Forces

  • Two different tensions, Tension 1 and Tension 2, are assessed for torque:

    • Part a: Calculate torque from Tension 1 using formula: Torque 1 = Tension 1 times Radius

    • Part b: Determine torque from Tension 2: Torque 2 = Tension 2 times Radius

    • Part c: Write an equation for the net torque on the pulley: Net Torque = Torque 1 - Torque 2

Problem 5: Wrenches and Torque Application

  • Analyze which combination of wrench length and force delivers the greatest torque to a bolt:

    • Different scenarios provided linking force, angle, and length.

  • Highlight the rationale for selecting the optimal combination based on torque equations.

Challenge Problem (Optional)

  • Participants are directed to resources on physicsclassroom.com to explore deeper problems.

Optional Extra Practice

  • Engage with Concept Builder Quizzes on:

    • Torque computation and direction prediction.

  • Additional practice and reflections on learning experiences from games and simulations related to torque.

In the context of torque, the mass of the hanging block is closely related to the gravitational force it exerts. Torque () is not just a function of the force applied but also the distance from the pivot point where that force acts.

  1. Force from Mass: The force exerted by the mass, due to gravity, can be calculated as the weight of the block (W = m0 * g), where:

    • m0 = mass of the block

    • g = acceleration due to gravity (approximately 9.81 m/s² on Earth)

  2. Torque Calculation: The torque created by this force when the mass hangs from a string wrapped around a disk can be expressed as:
    τ=R0×W\tau = R_0 \times W
    where R0 is the radius of the disk.

  3. Impact on Movement: If the tension in the string is less than the weight of the block, the net force acting on the block will lead to its downward acceleration. This means the torque created by the weight of the hanging mass contributes to the rotational motion of the disk, affecting how quickly it spins as the mass moves downward.

  4. Conclusion: Thus, the mass of the box is a critical aspect in determining the torque around the pivot point, as it creates the necessary force that drives rotational motion when combined with the distance from the pivot.