TORQUE-NOTES

Engineering Mechanics: General Physics 1

Page 1: Overview of Engineering Mechanics

• Introduction to Engineering Mechanics within General Physics.

Page 2: Concepts in Engineering Mechanics

• Engineering Mechanics: Study of forces acting on bodies and their movement effects.

  • Statics: Analysis of bodies at rest under equilibrium conditions.

  • Dynamics: Study of forces causing motion.

• Static Equilibrium: Object's state when all forces balance.

• Torque: Causes angular acceleration, critical for evaluating rotational dynamics.

  • Moment of Inertia: Measure of an object's resistance to angular acceleration.

• Rotational Kinematics: Concepts include

  • Angular Distance (rad)

  • Angular Velocity (rad/s)

  • Angular Acceleration (rad/s²)

Page 3: Objectives

• Objectives of the Course:

  • Determine rotational quantities for various systems.

  • Calculate moment of inertia and torque.

  • Apply rotational kinematics for constant angular acceleration systems.

Page 4: Rotational Motion

• Rotational Motion: Motion involving rotation around a center or axis.

  • Objects exhibit motion without moving from their initial location.

Page 5: Causes of Rotation

• Force Application Config6urations: Examines how a force changes a body's rotation based on its application point and angle.

  • Applied Force (Fi) affects the rotational behavior of a rigid body depending on its angle to the radius (r).

Page 6: Torque Explanation

• Torque (τ): Defined as the effectiveness of a force (F) to cause rotation about a pivot point (O).

  • Torque is produced when a force is applied at a distance (lever arm R) from the pivot.

Page 7: Torque Calculation

• Torque Formula:

  • τ = R * F

  • τ = R * F * sin(θ) (when considering angle)

Page 8: Non-zero Torque Condition

• For τ to be non-zero, vectors F (force) and r (distance from pivot) must not be parallel.

Page 9: Examples of Torque Calculations

• Example scenarios demonstrating how to calculate torque using the provided formulas with specific values.

Page 10: Direction of Torque

• Torque Direction Convention:

  • Positive when causing counterclockwise rotation

  • Negative when causing clockwise rotation.

Page 11: Net Torque and Rotational Equilibrium

• Net Torque: Critical for identifying system motion states.

  • If net torque (τ_net) = 0, system remains static or in rotational equilibrium.

  • If τ_net ≠ 0, the system rotates.

Page 12: Moment of Inertia Basis

• Moment of Inertia (I): Resistance to changes in an object’s rotational motion; depends on mass distribution relative to the axis.

Page 13: Moment of Inertia Formulas

• Common equations for calculating moment of inertia for various shapes:

  • Hoop: I = MR²

  • Disk: I = (1/2)MR²

  • Rod: I = (1/12)ML²

Page 14: Angular Motion Concepts

• Describes angular displacement, velocity, and acceleration akin to linear motion principles.

  • Angular Displacement (θ): Measure of rotation.

  • Angular Velocity (ω): Change rate of displacement.

  • Angular Acceleration (α): Change rate of angular velocity.

Page 15: Angular Motion Kinematic Equations

• Analogous kinematic equations for linear and rotational motion:

  1. ω_f = ω_i + αt

  2. θ = ω_it + 0.5αt²

Page 16: Examples of Angular Motion

• Sample problems calculating angular velocities and accelerations based on provided information, demonstrating problem-solving strategies.

Page 17: Conservation of Angular Momentum

• Angular Momentum (L): Product of moment of inertia and angular velocity.

  • Important for systems where net external torque is zero; L remains constant.

Page 18: Work Done by Torque

• Work calculated from torque and angular displacement:

  • Example: W = τ * θ

Page 19: Practice Problems

• Includes seatwork for students to practice calculating torque, moment of inertia, angular velocity, and momentum.

• Use of step-by-step solutions to illustrate effective problem-solving techniques.