Exam and Torque Summary

  • Third Exam Details:

  • Date: Tuesday, March 25, at 6:00 PM

  • Location: Refer to February 17 email

  • Requirements: UM ID (or other ID), #2 pencils

  • Closed-book, 75 minutes, multiple-choice (15 questions, no penalty for guessing)

  • Allowed: Three 3"×5" notecards (double-sided), calculator

  • Prohibited: Laptops, cell phones, smartwatches, communication devices

  • Scope: Sections 8.1–10.3

  • Torque Formula:

  • Magnitude of torque: ( \tau = rF \sin \phi )

  • Units: N·m

  • Torque Cases Comparison:

  • Case 1: Force pushing perpendicular at distance ( L/2 ) from axis

  • Case 2: Force pushing at 30° at distance ( L ) from axis

  • Torque is greatest in Case 1.

  • Rotating Bar Scenario:

  • As a horizontal bar with a hanging mass rotates to vertical, torque changes:

    • The magnitude of torque increases as it rotates.

  • Torque Direction:

  • Determined by the right-hand rule:

    • Clockwise vs. Counterclockwise distinctions affect direction using ( \tau = r \times F ).

  • Rotational Dynamics:

  • No total torque means no angular acceleration.

  • ( \sum \tau = I \alpha )

  • Moment of inertia depends on axis of rotation.

  • Acceleration of Wheels:

  • For wheels with different radii but same mass, the force comparison must be determined for identical angular accelerations.

  • Example Problem for Torque:

  • Block attached to a rope and disk that rotates due to gravity:

    • Torque on pulley is affected by tension in the rope and is typically less than mgR.

  • Problem Solving Procedure:

  1. Draw a picture.
  2. Identify independent bodies.
  3. Identify forces on each body.
  4. Draw free-body diagrams.
  5. Write Newton’s 2nd law in vector form.
  6. Choose a coordinate system.
  7. Rewrite Newton’s 2nd law in components.
  8. Identify constraints (e.g., a = Rα).
  9. Count equations and unknowns.
  10. Solve equations analytically (variables).
  11. Substitute values to find numerical answers.