Vernier Centripetal Force Apparatus User Manual

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LabQuest with Wireless Dynamic Sensor System (WDSS)

Start LabQuest App, let it auto-ID the photogate. Establish a Bluetooth connection to

the WDSS.

When using a photogate, you will need to set the position increment in photogate

motion timing to either 1/10 of the circumference (for tangential velocity) or 2π/10

(for angular velocity).

1. On the Meter tab of the LabQuest App, tap Mode.
2. Tap User Defined.
3. Enter the desired position increment as the User Defined value.
4. On this screen, choose the option to end the data collection with the Stop button.
5. Tap OK.
Collect force data with the WDSS and examine the graphs. For further analysis,

change one of your graphs to display Force vs. Velocity or Force vs. Velocity

Sample Data from the CFA

The following are summaries of experiments that you can perform with the

Centripetal Force Apparatus.

Centripetal Force with a Spin
To illustrate the capability of the CFA, here is a quick experiment using a different

perspective than is often used. Quite often, centripetal force is investigated using the

equation F=mv

/r, where F = centripetal force, m = mass, v = tangential velocity, and

r = radius of motion; however, a comparable equation is F=mr



where ω is the

angular velocity of the mass. This suggests an experiment that lets you explore a

variety of speeds with one run and with a very simple graphical result. If you simply

spin the beam by hand and let it slow down over 30 or 40 seconds, you will have

force as a function of angular speed. A graph of force vs. the square of the angular

speed is a direct proportionality, where the slope represents the product of the mass

and radius, since F=(mr)



The graph below shows two combinations of mass and radius. In each case, the slope

is the product of the mass and radius, and the functional relationship is

proportionality. A Vernier Photogate and Dual-Range Force Sensor were used, since

those will be most commonly available.

Centripetal Force with a Spin – a Detailed Look
The Vernier lab manual Advanced Physics with Vernier – Mechanics has an

excellent experiment that investigates F=mv

/r in a guided inquiry fashion. The

experiment is similar to the one mentioned above in that the students spin the

Rotating Beam and collect data as it slows down. A graph of F vs. v

shows a linear

relationship. They then vary the mass and determine that the F is directly

proportional to m. Next they compare runs with different radii and see that the force

is inversely proportional to the radius. The lab called “12A Centripetal Acceleration”

is also posted on our web site at www.vernier.com/accessories/cfa/

Moment of Inertia

You can also measure moments of inertia with the CFA. A beginning experiment is

to determine the moment of inertia of the entire rotating assembly. This

measurement is done by hanging a mass over the Ultra Pulley (which can be

attached to the side of the frame) and using a string to attach the mass to the 3-Step

Pulley on the Rotating Assembly. Allow the mass to fall, which applies a torque to

the system. Use a Vernier Photogate to measure the angular acceleration of the

system and then calculate the moment of inertia.

Attach the carriages to the beam and repeat the above experiment to determine the

moment inertia of this system and then determine the moment of inertia of the

carriages idealized as point masses.

Specifications

Encoder Wheel

10 spokes

Diameters of Pulleys on 3-Step Pulley on

Rotational Shaft

20 mm, 29 mm, 48 mm