Problem 6/110 animation

Problem No. 6/110 appears to be a relatively simple problem: the circular wheel rolls without slipping to the left. If the cm of the wheel were at the geometric center of the wheel, the wheel would roll with a constant speed, the normal force would be equal to the weight (constant) and the friction force would be zero (constant). 

However, this wheel has a "mass imbalance" with the cm G offset from the geometric center O. Watch the animation above. Note that as the wheel moves to the left,

• the speed is NOT constant. [This is due to the angular acceleration that you calculated for the wheel.]
• the normal contact force is NOT constant. [It fluctuates up/down in magnitude and is almost never equal to the weight. Can you see this in your solution? Consider how the y-component of acceleration for G varies with the position of G.]
• the friction force is NOT zero. [It fluctuates up/down in magnitude and left/right in direction. Can you see this in your solution? Consider how the x-component of acceleration for G varies with the position of G.]

Note that you are able to quantitatively predict this rather complex motion of the wheel using the Newton-Euler and kinematics. Visualizing this motion is more difficult.

End of the semester

All,

Thank you for your participation in the ME 274 course blog this semester, with particular thanks to those of you who posted and commented on the blog. We hope that the blog has proved useful to you in your studies in this course.

Attached is a summary of the usage of the blog in terms of number of visitors during the semester (nearly 22,000) and number of page views (over 50,000). From these statistics, it looks like the blog was used extensively during the times of exam preparation during the semester.

If you have suggestions on how the blog can be improved for better usage during future semesters, please let us know.

Wishes for an enjoyable summer,

Jeff and Chuck

Final Exam - solutions and statistics

• Click here for solution to MONDAY'S final exam.
• Click here for solution to WEDNESDAY'S final exam.
• Click here for final exam statistics.

Thank You

To both Professor Krousgrill and Professor Rhoads,

I just wanted to say thank you. I know both of you put a lot of time into teaching ME 274 this year. With all the extra office hours and the candy in class. I don't know about anyone else but I feel more intelligent after taking this class. My roommate is a biology major, and he thought g=9.18... Thank you again.

Mike M.

Final Exam Last Minute Question

I cant remember which it was, so in the case of a ring and a circle of the same mass rolling down an incline, which will gain a greater velocity first and why? I believe it is the circle due to a smaller I, but I am not sure.

Slipping Disk Friction Work

So when a disk is slipping and there is a friction force. Does the friction do any work?

Problem 8.46

I am having trouble in solving this problem.

Firstly, which bodies do I take as 2-force members.

Then, small oscillations about which point should be taken?

Multiple choice questions

Click here for a PDF file giving suggestions (thought processes) for the sample multiple choice/short answer questions covered in class on Friday.

Let us know if you have any questions on these.

Final Exam - sample multiple choice/short answer questions

Click here for sample multiple choice and short answer final exam questions.

Exam No. 3 - Statistics

Click here for Exam No. 3 statistics.

Problem 8/72

How do you come up with the equation for the force? I am guessing the frequency is just 1/T found from the equation of the road, but I am coming up with something way off.

Final Exam - Review materials

Click here for final exam review materials.

Exam No. 3- Solution

Click here for the solution of Exam No. 3.

Sample Exam Problem 24

OK. I need help on this one. So far I was able to write the Newton-Euler formulas but that's it. I am left with 4 unknowns (T_ad, T_eg, a_gx, a_gy) and tried using kinematics for the bar to relate a_a and a_g but that doesn't seem to help much.

I know the bar is somehow going to swing to the right and go down, but are pt. A and pt. G constrained to a particular type of motion (i.e. horizontal or vertical)? Anyone have any idea on what I'm missing? Your help is appreciated.

Exam No. 3 - Review material

Click on this link for Exam No. 3 review material.

Problem No. 6/121 - erratum

An error in the solution video for Problem 6/121 has been brought to my attention. When calculating the total mass moment of inertia about point C for the wheel, I said that 1 + 1 = 3/2 (see above figure). "2" is the more commonly accepted answer for that sum ...

Please accept my apologies for the error, and thanks to those who pointed out the mistake.

8.130

I am having trouble with this problem. I found the basic EOM in terms of M*X_dot_dot+K*X=0. I think what I need to do next is to find the sin/cos equation for x(t) using x-0 for the amplitude (the C or S in the basic equation x(t)=Ccos(wnt)+Ssin(wnt) )... How do I go about finding this equation?

Problem 8/9

In this problem, I have the frequency equal to sqrt(k/m). If this is correct how do I go about solving for k so that i can solve for the frequency itself? Thanks.

Oscillation of bar due to gravity

If we consider the following equation:

squareroot ("K"/"M") where K=mgd and M=Io+md^2 P.A.T.

We know that Io=((1/12)mL^2 for a bar and we can symplify the following equation:

squareroot((mgd) / ((1/12)mL^2 + md^2)) which is also:

squareroot((mgd) / (m((1/12)L^2+d^2)))

and so we see that the mass cancel out of the equation and we get:

squareroot(gd / ((1/12)L^2 +d^2))

This work also if Ic=Io .

So we can conclude that the mass does not affect the equation for the frequency and consequently; we estimate that the frequency will stay the same for whatever mass we used at G.

Homework Hints: Vib-3

• FBDs: It is recommended that you draw individual FBDs for the drum and block. Choose a translational coordinate for the block; e.g., "y" measured positively downward. In drawing the FBD's, recall that the tension on both sides of the drum are NOT equal (due to the rotational inertia of the drum).
  
• Newton-Euler: Use Newton in y-direction for the block. Use Euler for the drum.
• Kinematics: Relate the translation of the block (y) to the rotation of the drum (theta).
• EOM: Combine your two Newton-Euler equations with the kinematics to obtain a single differential equation of motion (EOM) for the system in terms of theta and its time derivatives.