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Equipment Needed

* Computer with access to the internet
e Timing device (e.g., stopwatch on smartphone)

For the first six chapters, we considered linear motion: displacement, velocity, acceleration, linea
momentum. Time for a curve ball. Rotation is as much a part of our everyday life as linear motion. Earth
otates, giving us our days. Wheels on our cars ca
y us to Sta
ucks. Hipsters listen to vinyl albums on thei
overpriced turntables. The concepts behind rotational motion are fundamentally the same as with linea
motion. We have angular displacement (measured in radians):

26 =6,-6,
Angular speed (measured in radians per second):
A0 6; —6;
Wapg = —=
CITA tt;
Angular acceleration (measured in radians per second squared):
Aw wp —w;
Aapg = — = ————
PITA tt;
The relationships between linear quantities and angular quantities summarized as follows:
| s The quantity s is the arc length created by an
Displacements: s=0r f= 5 i i
7 angle 6 on a circle of radius r. The quantities v,
Speeds: v= or .. and a; yefey ic tangential velocity and }
z acceleration, respectively. Think of “tangential” as
Accelerations: a, = ar a= a the linear component of rotational motion at
some instant in time.

Recall that acceleration is a change in velocity over time. When discussing linear motion, we considered only
changes in the magnitude of velocity (an object had acceleration if it was speeding up or slowing down). Fo
otational motion, velocity also changes when the direction of an object's motion changes. An object will have
acceleration if its velocity changes direction, even if the magnitude of the velocity is constant. Isaac Newton
told us that if an object has non-zero acceleration, then it must also be subject to a net force. So, if an object is
changing directions, there must be some force that is causing that directional change. For rotational motion,
we consider the force that keeps an object following a circular path, and we refer to this force as the
centripetal force, F;, and the accompanying acceleration is centripetal acceleration, where:
F. = ma,
An expression for centripetal force in terms of tangential velocity and the radius of the circle is:

This lab will explore rotational motion, particularly the relationships between radius, speed, acceleration,
mass, and centripetal force.
Part 0: Explore the Simulation

1. Open the following simulator:
2. You can (and should)maximize the simulation by clicking the double a
ow button in the upper-left
corner (which inconveniently overlaps the “Reset” button).
Click your “Esc” key to exit full-screen mode.
3. Optionally, you can click on the “Velocity” and
“Acceleration” buttons to enable visual representations of
velocity and acceleration vectors.
4. Click on the “Start” button in the upper-right corner of the
orange panel.
a. Don’t click any of the other ga
age on the webpage.
5. The object will start rotating. Adjust the speed, radius, and Speed whi > A re tot
mass and observe how velocity, acceleration, and force Radius P v
change. 0
Uniform Circular Motion ~~ sts
Acceleration: 13 m/s/s
Net Force: 133 N
p Velocity
[| oe 'S PL

Check the following:
® Set Speed to 10 m/s, Radius to 60 m.
® Start the simulation.
e Measure the time it takes for the object to rotate one time. Record that value below:

Part 1a: Estimate the Radius

0 4a
Set Speed to its minimum value (Vg, = 10 m/s). This is tangential speed.
Set Radius to its maximum value (7g, = 60 m).
Start the simulation.
Using a stopwatch, measure the time it takes for the object to make one complete revolution. Record
your result below.
Repeat this measurement two more times and record your results.
Find the average of your time values and record this as £1.59
Calculate angular speed using your average time, where:
Recall that for one complete revolution, A@ = 2m. Record your result as @;.60-
Calculate the radius of the object’s motion, noting that:
Vsim = WF

Repeat steps 4 through 7 with the following values:
* Vim =30m/sand rg, =60m = w3g.60
* Vim =10m/sand rg, =30m = woz
® VUsim =30m/sand rsp; =30m = w30:30
Vsim (M/S)



10 Ws0.60 (rad/s) Teate (M)
it 2 60°


W3o.60 (rad/s) Teac (M)


Average £19.30:
i930 (rad/s) Teac (M)

W30:30 (rad/s) Teac (M)
Part 1b: Cleaning Up That Mess
You may have noticed that there is a discrepancy between the radii reported in the simulation and the
adii you calculated. The simulation seems to have an undocumented and e
oneous scaling factor in thei
Find the conversion factor required to convert 74; to 75m. This is the constant that you multiply 7.4; by
to yield 75;,,. For instance, if you calculated 7.4; = 10.0 m for ry, = 5.00 m, then your equation would
e 75m = XXXXXXXXXX,4 and your conversion factor would be C = XXXXXXXXXXIf your conversion factor is
different for the four cases above, use the average value.
Tsim = C+ Teare

What's interesting about that C; value? If the value doesn’t look familiar, you may have done something
wrong in your calculations. Find and fix your e
Part 2: Rotational Motion Sudoku
It’s not really sudoku.

Fill in the table below using your wits and the following equations:

FE =ma. =
a =—
Round your answers to one decimal place. When you've completed the table, enter the quantities for each
ow into the simulation and verify your results. Co
ect anything that requires co
ection, keeping in mind that
the simulation rounds to the whole number.

Speed Radius rey A
Vsim (M/S) Tsim (M0) LCT) [PCD
10 38 8
Answered Same Day Feb 28, 2024


Bhaumik answered on Feb 28 2024
13 Votes
Part 0: Explore the simulation
· It took 12.29 seconds for the object to rotate one time.
Part 1a: Estimate the radius
· For vsim 10 m/sec & rsim 60 m, the time recorded is: 12.29 seconds
· For vsim 30 m/sec & rsim 60 m, the time recorded is: 3.92 seconds
· For vsim 10 m/sec & rsim 30 m, the time recorded is: 5.91 seconds
· For vsim 30 m/sec & rsim 30 m, the time recorded is:...

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