Exam 3 Review Notes

Exam 3 Review

General Information

• Exam 3 is one week from today.
• Covers material from lecture 6B (linear kinetics energy) through 9A and 9B (whatever is covered).
• Exam in class on Thursday.
• 20% of course grade.
• Closed book and notes.
• Standalone calculators allowed.
• Scantron based: dark pen or pencil required.
• Two-page equation sheet and two-page set of plots will be provided.

Provided Plots

• Plots are similar to previous ones, with adaptations for angular kinematics.
• First page: bicep curl conditions, forearm segment angle (90 to 270 degrees and back).
• Qualitative derivative: hill, valley, then hill valley, valley hill.
• Vertical lines: represent when forearm and hand are horizontal.
• Joint angle: included elbow joint angle (largest when joint is open, smallest when closed).
• Starts close to 180 degrees, drops to a small value, then opens again.
• Slope is negative, so negative velocity has a valley, positive slope has a hill.
• Elbow extension joint angle: increases as you extend the joint.
• Flexion joint angle: increases as you flex the joint (excluded joint angle).

Exam Structure

• 55 total questions.
• 20 true/false at 1.5 points each.
• 35 multiple choice at 2 points each.
• Questions will assess memorization, understanding of concepts, and problem-solving skills.
• Some questions involve symbolic problems, others involve numerical calculations.

Material Covered

• Linear kinetics energy (Lecture 6B): work-energy relationship, springs, and strain energy.
• Angular kinematics and kinetics.
• Material through 9A and 9B.
• Number of questions per section is proportional to the section's length.

Exam Taking Strategy

• Aim for about an hour to complete the exam.
• Goal is to avoid a large curve (ideally no curve or a small one).
• If you do better on exam 3 than exam 2, exam 2 grade will be replaced with the average of the two.

Moving Day

• Exam 3 is referred to as "moving day".
• Goal is to position yourself well for the grade you want by the end of the course.
• After exam 3, exam 2 will be finalized; exam 4 (final exam) can improve exam 3 score if you do better on it.
• This exam represents a significant portion (75-80%) of the course grade.

Review Slides

• 6B: Work energy
  • Lost energy is always added back in as a positive value.
  • Consider initial conditions and affected terms.
• Springs
  • Hooke's law: Describes the spring force as a linear relationship with displacement. \F = -k * delta x, describing the force required to hold the spring at displacement "delta x" from its resting position, where k is the spring constant.
  • Work and energy of a spring being equal to each other: \frac{1}{2}k \Delta x^2.
  • Average force to stretch a spring is half the force required to hold it at that extension due to the linear increase in force.
• Angular kinematics
  • Basics, segment angles, joint angles, linear and angular relationships.
• Angular kinetics torque
  • Moment arms.
  • Torque as the resultant force times a moment arm.
  • Cartesian components.
    • Vertical component of the Cartesian, your moment arm is going to be a horizontal distance to that.
    • Horizontal force, then your moment arm is going to be the vertical.
    • Subscripts on the moment arms go with the force that they belong to.

Applying Newton's Laws

• 8B: Applying Newton's laws, free body diagram.
• 9A & 9B (SJS): Simple/Single Joint System. The role of SET-nine is to continue to work our way into the body and be thinking about how the moment arms of our muscles, our individual muscles might change as we move
  • Analyzing how moment arms of individual muscles change with movement.
  • Understanding how muscles operate across joints.

Practice Sets and Quizzes

• Practice sets: important for exam preparation.
• Supplemental practice set for linear energy.
• Canvas quizzes: review and understand the questions.
• Modified versions of quiz questions may reappear on the exam.

Additional Resources

• Content from class.
• Supplemental practice set.
• Canvas Quizzes.

Finishing 8B

• Generalized free body diagram: Simplifies diagrams by replacing linear effects with a joint reaction force.
• Joint reaction force: Acts at the axis of segmentation and doesn't produce torque in angular equations.
• Net Muscular Moment: Encapulates all of the external forces that gets exposed and torque producing capabilities.

Net Muscular Moment

• Represents the sum of torques generated by muscles crossing a joint.
• Positive: flexor torque, Negative: extensor torque.
• Net Muscular Moment = Summation(Torque{flexors}) - Summation(Torque{extensors})
• A positive net muscular moment (e.g., 100 Nm) indicates net flexor activity.
• Antagonistic torque often present for joint stability.
• EMG can help determine individual muscle forces (beyond the scope of the class).

Equation and Free Body Diagram

• External forces generate linear equations.
• Torque is included in the angular equation.
• Equation for motion about the elbow joint includes muscle torque and torque due to weight.

Quasi-Static Conditions

• Assume linear and angular accelerations are zero.
• Net muscular moment equals torque due to weight of forearm, hand, and barbell.

Profile Shape (WRW)

• Profile: hill then hill.
• Greatest torque when forearm and hand are horizontal.
• Least torque when extended or flexed.
• Concentric action of flexors when raising, eccentric when lowering.
• Uniphasic muscle activation.

Dynamic Movement

• Acceleration is present but not dominant.
• The I alpha term is added to modify the quasi-static profile.

Impact of Acceleration

• I alpha (hill valley valley hill) overlaid on the WRW profile.
• Enhances needed torque in the first half of the up phase, reduces it in the second half.
• Profile shifts to the left.
• During the down phase, the opposite occurs.
• Still all flexor torque, uniphasic.

Ballistic Movement

• I alpha term is dominant.
• Requires both above-zero and below-zero components.

Up Phase

• Large hill with a small valley.
• Need extensor torque to decelerate.
• Biphasic muscle activation (agonist first, antagonist second).
• Possible triphasic activation.

Down Phase

• Extensor torque to start, followed by flexor torque.
• Biphasic muscle activation.
• Possible triphasic activation.

Overall

• Slow movements have clean hill profiles.
• Acceleration manipulates these profiles.
• Ballistic movements show significant manipulation and biphasic/triphasic activation.

Angular Acceleration

• I alpha oscillates around zero.
• Positive acceleration is counterclockwise, negative is clockwise.
• Adding I alpha to the quasi-static profile enhances the positive and negative components.

Horizontal Plane Movement

• No WRW term.
• Net muscular moment equals I alpha.
• Hill Valley Valley Hill profile.
• Biphasic activation (flexor followed by extensor).
• Potential triphasic activation.

Angular Work and Power

• Angular work: WorkA = Torque{avg} * \Delta \theta
• Angular power: PowerA = \frac{WorkA}{time} = Torque{avg} * Velocity{angular}
• Instantaneous power: Power{instantaneous} = Torque{instantaneous} * Velocity_{instantaneous}

Newton's Third Law (Angular)

• Equal and opposite torques.
• A muscle generating torque on one side of a joint creates an equal and opposite torque on the other side.
• Often not observed due to restrictions at other joints.

Simple Joint System (SJS) / Single Joint System

• Simplifies complex joints and muscles to understand muscle force and joint stabilization.
• One limb, one muscle (muscle tendon complex), one joint.
• Focuses on how muscle moment arms change through the range of motion and influence force needs.
• Often treated as a quasi-static system to eliminate the acceleration term.