Topic: HW 8b #2
After fixing a flat tire on a bicycle you give the wheel a spin.
(a) If its initial angular speed was 6.52 rad/s and it rotated 15.7 revolutions before coming to rest,
what was its average angular acceleration?
(b) For what length of time did the wheel rotate?
Dr. Man: Notice that 1rev = 2*3.14 rad. Convert delta_theta in to SI unit rad before you plug
in numbers. Notice the direction and sign of acceleration .
Everything else is like constant acceleration in chapter 2. See the sample question on lecture notes.
Student A: I converted the revolutions to radians, and then divided by the angular velocity to
get the time. I then divided the change in omega with the change in time. Not sure where
I'm going wrong..
Dr. Man: There is angular acceleration. As a result,
total angle covered = omega_0 * t +1/2 alpha t^2
You mixed it with constant angular velocity question. Check out the equations (very similar to
constant acceleration motion) listed on the lecture notes and find the useful ones.
You converted the revolutions to radians, and then divided by the angular velocity to get the time.
What angular velocity did you use? Remember that it slowed down. Obviously, you can not
use initial angular velocity. You can use average angular velocity though, to find time.
Topic: HW 8b #6
Dr. Man: The object shown below (length = 6 m) remains completely stationary, despite the
fact that three forces act on it. Forces 1 and 3 act at either end, while force 2 acts 1/4 of the
way from the left end.
new-torque-prob
If the size of force 3 is 3 N, then how large must the other two forces be?
F1 =
F2 =
(For excellent practice, see if you can also get these answers using different pivots!)
Some people asked me this question:
"dont we need to know the mass?"
Here there is no mass, just a few forces. You can consider this is a top view on a frictionless
table. Mg and Normal forces are canceled. You can play this torque balance on a table
using a pencil, two hands and another force actor..
Forces create torque and torque needs to balance. Total torque needs to be zero for equilibrium.
Imagine you are playing a game with your friend. You use two hands to push forward ( F1 and F3 )
at the edge, and your friend use one hand to push in the middle part. How can the three forces
be balanced so that total force is zero, and total torque with respect to any possible rotating
point is zero?
Set your equations of Total force= 0
and Total Torque = 0.
Keep in mind that CCW and CW torque have different signs.
Second Question:
"I am still not sure about question one, isnt F2 supposed to be zero because it is the pivot point? "
If you choose point 2 to be the pivot point, the TORQUE of force 2 is zero because it goes
through the pivot point, not that F2 is zero. Again, choose ONE pivot and set total torque =0
and total force =0. Solving those equations, you will find all forces and you can verify your answer
using another point as the pivot. The answers would not change.
Topic: 8b #7
Student A: Below is a diagram of a baseball/forearm system at rest. It is acted on by four
different forces: the weight of the forearm, the weight of the baseball, the bicep force, and a
force from the upper arm bone (attached at the elbow).
Part of the question asks about the force of the upper arm bone on the forearm. Is the upper
arm bone perpendicular to the forearm? Does it play a role in net torque considerations?
Dr. Man: Great question. The upper arm bone goes through the axis, which is the elbow,
as a result, force from the upper arm bone's torque is _____________?
Recall the normal force in the sample question we solved toward the end of today's class.
See the lecture note. But keep in mind that even if the force of the upper arm bone
doesn't contribute to torque, it can contribute to total force to make total force =0 for your equilibrium.
That's how you can find its direction and size.
First identify the elbow to be the axis of rotation.
F bone goes through the axis, its Torque =???.
Also, you know how to write the torque for the bicep force.
For the arm gravity torque, its moment arm is L/2.
While the bass ball gravity torque = ____?____*mg ?
Pay attention that the base ball has small m not the big M.
At the end, distinguish those CCW torques and CW torques.
By setting the total torque = 0, you will find F bicep, though you still don't know F bone.
For the force acted by the bone, try to figure out its direction first.
All the other 3 forces are in vertical direction (y direction), so if the bone had some
horizontal push to the forearm, there is no way to make the total force = 0, right?
So the bone's force on the forearm must also be vertical, up or down? How many newtons?
Keep in mind for static equilibrium and the total force on your whole system
(arm, and baseball) = 0
By setting the total force = 0, you will find F_bone.
Topic: 8b #8
Student A:
To determine the location of his center of mass, a physics student lies on a
lightweight plank supported by two scales L = 4.50 m apart, as indicated in the figure below.
(a) If the left scale reads 252 N, and the right scale reads 110 N, find the student's mass.
In drawing this diagram, do we also draw a normal force point up? What is the moment
arm of N? If I consider this in net torque, there are two unknown variables.
Dr. Man: Identify your system. Your system is the student AND the plank, even though
your plank has little mass. Consider student and plank as a whole.
What are all the forces acting on the student and the plank?
Mg, where does Mg acts?
N, how many Normal forces do we have here? Two support!
So three forces, very similar to question 6.
(keep in mind that total torque is zero no matter which point you choose to be the axis;
left end, right end, mass center...)Because it is not rotating with respect to any of those points.
Total torque with respect to any ONE of those axis is zero.
Just don't mix torques for different rotation centers. Once you choose one rotation axis, stick
to it until you solve the problem.
You will need equations that total torque =0 and total force =0
Student A: Does that mean Mg acts L/2?
Dr. Man: Since the body is not uniform, the head is heavier than the foot, so you don't know
whether the mass center is. You can set Mg's location at x and find it out, by choosing the
left end as the rotation axis.
Again Total force=0 and total toque =0.
Since you know both N, you can easily find mg first.
Student A: Thanks Professor Man. I found the mass of the body, but I'm having some
trouble with the second part of the question asking about the center of mass. I tried finding
it using the method described for calculating COM in lecture, but I realized I don't know
where M is acting. I'm not even sure if I need M to find the COM. Where should I set
the axis?
Dr. Man: To use the COM formula, you need to know how mass is distributed, such
as two balls or 10 balls can be treated as 2 points or 10 points. In this one,
since the body is not uniform, you can not assume mass center is at L/2.
As I said, first draw all forces acting on your object of interests( Mg, N1, N2)
You need to draw N1 and N2 at their correct location.
Mg is always acting through the mass center, downward.
You assume Mg is at distance x away from the left end.
First, considering total force =0, you can easily find Mg.
Then, since you figured out how many newtons all the three forces are, you should be able
to find where Mg needs to be in order to keep total torque =0
(pick the left end to be the rotation center, for example)
You can verify your results by choosing the right end to be rotation center later.