You will need to use the text book for this problem set. If you do not have access to a copy, you can use the online google book version which you can find through Mirlyn or via this link

The Parallel axis theorem is used to find the moment of inertia at a different point of rotation.

where is equal to the mass of the object in kg and is equal to the perpendicular distance between the CoM and new point of rotation.

The table you will use for this problem set (table 2.6) gives the moment of inertia about the CoM of the segments. The somersault axis represents the transverse axis and is the axis of interest for problem 6.

In problem 5, the coefficient of drag is given as this is not correct, the coefficient does not have units ()

The production of work based on oxygen consumption is

I highly recommend putting in your units when solving problem 5.

In table 2.5, you are given an average segment length for men and women (in cm), but a segment weight as a percentage of the subject's body weight and the location of the CoM as a percentage of segment length.

In problem 6c, you need to find the angle between the muscle and the arm in order to calculate the moment arm of the muscle (I recommend using a diagram to find the angle).

Here are the instructions for turning in problem sets, this is important to follow not only for grading turn around time, but also because it is good practice for this type of problem solving.

Please note, you will not get full points if you do not follow these instructions - having the correct answer is insufficient, the proper steps need to be included as well.

• Include your name and section number on the first page
  • Wednesday 2pm - 006
  • Thursday 3pm - 007
  • Thursday 4pm - 008
  • Friday 9am - 004
• Each new question (number) must be started on a new page. The different parts of a question (letters) can continue on the same page as long as they are clearly distinguishable.
• Each part of a question (letters) must follow all six steps. Label each step.
• When a question contains multiple parts (ex. a, b and c),
  • in step 2 of the first part (a) you must included all variables given in the problem, as well as your drawings (free body diagram and reference frames are required, sketches are highly recommended)
  • in the subsequent parts (b, c, etc...) only the variables needed to answer the question need to be included (make sure to add the values of the previous answers).
  • if the drawings for these section (b, c, et would be the same as that from a previous section, you do not need to redraw them - if the previous drawing is insufficient, included the new drawings in step 2
• Before adding numbers to an equation - the variable you are solving for must be isolated (alone on one side of the equation).
• Equations must be aligned vertically (preferably with the equal signs in line).
• Points will be taken off for any scribbles or crossed of sections (recopying your problem sets is highly recommended, not only so that they look neat, but because it will help you to understand to problem better!)

If you have any questions about these instructions, please contact me.

and remember - a happy grader equals better grades :)

Be aware of your units:

Be sure to answer the questions, for example in question 1 are you asked for the force of the swimmer or the force of the water?

Line up your reference frame according to the vertical, medial-lateral and anterior-posterior axes of the human.

When dealing with a projectile motion, remember that there are forces acting in the vertical direction, but not the horizontal direction. You must separate a velocity into its vertical and horizontal components before calculating changes in velocity.

With a projectile motion, the vertical velocity of the object when it has fallen back to its initial height will be equal and opposite to the initial vertical velocity.

There are questions which are best split into parts, for example in question 3 consider the jump, the dive and the landing in water as three separate problems (each have their own initial and final velocity).
This also applies to question 4.

The graphs for question 5a) need only be qualitative – no need for calculations. However you need to include numerical values to the axes. (I would suggest doing parts b and c before drawing the graphs to have a better idea of what the movement will look like)

Flexion is considered a negative movement.

When acceleration is constant, the same equations used for linear movement can be applied to angular movement, for example

A free body diagram includes only the segment of interest and the external forces.

Kinetic Energy:

Potential Energy:

Total Energy:

Mechanical Power:

Conservation of Mechanical Energy:

If there are no nonconstant forces () then

and therefore

Energy and signs
When working with Energy (rather than vectors) you can use absolute values, however you must than keep track of whether your answer is positive or negative (ex. has the potential energy increased or decreased, is the speed positive or negative)

Friction
Friction is a force (N), U is energy (Nm). In order to determine the effects of friction on the total energy, you must consider the distance it was applied over.

To calculate friction, you must use the force which is perpendicular to the surface (normal force).

Anthropometric Table

There is a table in your text book which lists estimates of the weight and location of the center of mass of various body segments. Remember there is a difference between weight and mass. Also be sure to indicate from which joint you are giving the location of the CoM.

Angular Motion

Linear velocity is a function of angular velocity and the distance from the center of rotation

represents the change in magnitude of and accounts for the change in direction of

You can determine if an angular velocity is positive or negative using the right hand rule - curve your fingers in the direction the object is rotating, if your thumb points down the velocity is negative, if it points up it is positive.

In order to use these equations, you need to have your angle values in radians. Radians are special in the sense that if you multiply something with a unit (example meters) by a value in radians, your answer will not have radian as a unit.

One last hint - if you throw something from a moving car (do not actually do this!), you need to add the velocity of the car to the velocity you threw the object with in order to get the velocity of the object relative to the road. Depending on if you throw the object in the same direction as the car is moving or in the opposite direction, the velocity of the object will be faster or slower.

Problem set 2

Q Do you have to show your work for questions 1-26 ?
A No, you do not have to show your work, but make sure you understand why something is true/false, a/b/c/d/e. For questions 27-29 show your work in the 6 steps.

Problem set 1

Q Do you need to indicate the number of each step (ex. “step 1”)?
A Although this is not required, I recommend doing it to keep your homework as clear as possible

Q Do you have to repeat steps 1 and 2 for the second portion of a question (i.e. if you wrote them in a, do you need to write them again for b)?
A For problem set 1, repeat steps 1 and 2 for each portion of a question (we can discuss this for future problem sets)

Q For question 8, do you have to do the graph by hand, or can you do it by computer?
A You can do question 8 either by hand or computer.

Q For question 4, do you have to show the calculations if the answer is in the text book?
A *** modified answer*** see optimal angle post

Q Does the homework need to be written in ink?
A The homework does not need to be written in ink, pencil is fine. Just make sure that it is neat!

Q Is green engineering paper required for the problem sets?
A No, any type of paper (within reason!) is acceptable.