Uniform Circular Motion

PHYS 1111L/2211LIn this lab you will investigate how the centripetal force, the radius, and the massaffect the motion of an object going in a circle.EquipmentRotating platform and baseCentripetal force accessoryMass hanger and massesPulleyStringTimerSetupNOTE: Throughout the setup and performance of the lab, it is recommendedthat you follow a “reader/doer” procedure. One person in the group readseach step of the procedure out loud. After each step is read, another personperforms the step and verifies that it is complete. Other individuals in thegroup watch to verify that this procedure is followed correctly.1. Level the apparatus with the leveling screws until the platform is level in alldirections.2. Pick up the hooked object and remove the plate on each side (see the diagrambelow). Measure and record the mass of the center piece (the one with thehooks).3. If it is not already assembled, assemble the side post in accordance with thefollowing diagram and directions (see next page).Uniform Circular Motion 5/12 2

PHYS 1111L/2211LNOTE: in this procedure, we will use m to denote the mass of the threehookedobject (spinning mass), and M to denote the mass hanging from thepulley (hanging mass).6. Loosen the clamp that holds the side post and slide it along the platform untilthe threads supporting the hooked object are exactly vertical. Use every deviceat your disposal to ensure this.7. Clamp the side post in place (on the left side of the center post) and record itsdistance from the center of rotation. This is the radius. See the diagram below.The hooked mass is the thing that is spinning, and the axis of rotation is thecenter of the center post (the rotating shaft).8. Move the indicator bracket on the center post until it surrounds the pink ring.The apparatus should now look like this (see Figure 1):9. Remove the hanging masses and hanger, the pulley, and the thread from theouter hook on the hooked object. Note that the spring now pulls the hookedobject toward the center. Recheck whether the setup balances and adjust asnecessary.Lights, Camera, ActionUniform Circular Motion 5/12 4

PHYS 1111L/2211LGrasp the knurled portion of the shaft and rotate the platform. Increase the speeduntil the pink ring is once again inside the indicator bracket. Practice until you cankeep the platform rotating uniformly (constant speed).Now you are going to perform two different procedures:• In the first you will keep the radius and spinning mass constant whilevarying the centripetal force.• In the second you will keep the centripetal force and radius constant whilevarying the mass of the hooked object.Variable Centripetal Force (Radius and Spinning Mass Constant)1. Start timing at some convenient, reproducible point and measure the time ittakes for the platform to spin completely around ten times. Do this three times andrecord all three results.2. Replace the pulley and string, this time with 75 g instead of 100.3. Now the string holding the hooked object will not be vertical. In order toreturn it to vertical, take the top bracket attached to the spring on the center post(see Figures 3 and 4) and move it down until the string holding the hooked objecton the side post is again vertical. Make sure the indicator bracket is around thepink indicator ring. Do not change the radius.4. Remove the pulley, 75 g, and string.5. Spin the apparatus as before, for ten revolutions, three trials total.6. Repeat the above steps with 50 g hanging from the pulley and again with 25 g.Variable Spinning Mass (Radius and Centripetal Force Constant)1. Return to steps 5-9 in the setup (see page 3), hanging 50 g on the pulley thistime. Realign the setup as in step 3 just above.2. Remove the pulley, mass, and string, and spin the apparatus for ten revolutions,three times total.Uniform Circular Motion 5/12 5

PHYS 1111L/2211L3. Add one of the side plates to the three-hooked object. Measure and record thenew mass, and repeat the entire procedure. Then add the other side plate, measureand record the new mass, and repeat again.Calculations1. Calculate the angular speed ω for each data point as follows:• Divide 10 revolutions (assuming you took data for 10 revolutions) by theelapsed time. This gives you an angular speed in revolutions per second.• Multiply this number by 2π to convert to radians per second. ω = 2π(10)/t2. For each data set, calculate the average angular speed ω, the deviation of eachone from the average, and the average deviation (a.d.).• Deviation = measurement minus average, dev = x i - x avg• Average deviation = average of absolute values of deviations∑ xi− xavga.d. =N3. Determine the direct value for the centripetal force:• F = (total hanging mass M) x g• Don’t forget to include the mass of the hanger if you used one.4. For the variable centripetal force procedure:• Graph the centripetal force versus the square of the angular speed ω, that is,F on the ordinate (y-axis) and ω 2 on the abscissa (x-axis).• Draw the best-fit line and calculate its slope.• From the slope, calculate a value for the mass of the hooked object.Uniform Circular Motion 5/12 6

PHYS 1111L/2211L• Compare your calculated value to the measured value (measure the mass onthe triple-beam balance if you have not already done so). Calculate thepercent difference between your measured and calculated values.5. For the variable spinning mass procedure:• For each data set, using the average angular speed ω, calculate thecentripetal force using Equation 3 (F = mrω 2 ). Recall that m is the mass ofthe three-hooked object, r is the distance from the center of rotation, and ωis the angular speed you just calculated.• Determine the percent difference between this value and the directlycalculated value for F (F = Mg). [Percent difference = difference, dividedby the average of the two, times 100%.] [% diff = (diff/avg) x 100%]6. (2211L only) Perform uncertainty analysis as follows:• Consider the formula F = mrω 2 .• Choose one of your data sets from the variable mass procedure.• Estimate and justify uncertainties in your measurements of m and r.• Using those estimates and the average deviation of the angular speed,calculate the uncertainty in F.• Does your value of F = Mg fall in the range of the value from the formulaabove, plus or minus its uncertainty?• Which of the three terms in the equation is most important to measureaccurately? (That is, which term, if any, dominates the calculation?)QuestionsSuppose the Moon orbits the Earth in uniform circular motion, making onecomplete revolution in 27.3 days. If the Moon’s orbit around the Earth has aradius of 384,000 km, what is the Moon’s orbital speed?A standard audio CD is played in a drive (called a CLV, for constant linearvelocity) that passes the data tracks on the CD under the read head (the laser) at aconstant linear speed. Does the CD spin at a uniform angular speed? Explain whyyou believe it does, or does not. If you believe it does not, determine whether itspins faster when reading the inner or outer tracks. Explain your answer.(2211L only) Answer questions 4 and 5 in Cioffari lab #7.Uniform Circular Motion 5/12 7

PHYS 1111L/2211LData Sheet - Variable Centripetal ForceMass of hooked object m____________ radius of rotation _____________Total hanging mass M_______________ F = Mg ____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgTotal hanging mass M_______________ F = Mg ____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgTotal hanging mass M_______________ F = Mg ____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgTotal hanging mass M_______________ F = Mg ____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgCalculated mass of hooked object_______ Percent difference ____________Uniform Circular Motion 5/12 8

PHYS 1111L/2211LData Sheet – Variable MassMass of hooked object m ____________ radius of rotation _____________Total hanging mass M_______________Trial Number of turns Elapsed time Angular speed ω DeviationAvgF = mrω 2 ___________ F = Mg ____________ Percent difference ____________Mass of hooked object m____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgF = mrω 2 ___________ F = Mg ____________ Percent difference ___________Mass of hooked object m____________Trial Number of turns Elapsed time Angular speed ω DeviationAvgF = mrω 2 ___________ F = Mg ____________ Percent difference ____________Uniform Circular Motion 5/12 9