Experiment 8: Rotation
Part one:
You will check whether s = r θ correctly predicts the distance moved by the 25 g mass in the system
shown. Measuring the diameter of each gear or
reel with a vernier caliper gives their radii. From
this and the fact that the 1 kg will move 2 cm,
repeatedly using s = r θ gives the distance moved
by the 25 g. You will then measure this distance
and compare to what you calculated.
Hang 25 g from a bent paper clip tied to the larger
reel’s string. The weights have circular holes
which stay on the paperclip better than hanging
them by thir slots. Put 1 kg on the other string.
Measure the average diameter of each gear, using
a vernier caliper to get hundredths of a centimeter,
as shown. (To the tips of the teeth is too much, to
the bases is too little.) If you forgot how to read a
vernier caliper, refer back to experiment 1A.
On the reels, measure the diameter which the string unwinds from, putting
the caliper jaws in where the string is, not on the rim. Show the radius of
each on the data sheet.
Suppose that the 1 kg load is lifted up 2.0 cm. Under CALCULATIONS, find how far the 25 g
drops by the following chain of calculations:
First, look at wheel A. From SA, the distance moved by a point on its edge (which equals the
distance moved by the 1kg), and rA its radius, find θA, the angle it turns.
Next, look at gear B. θB, the angle turned by B equals θA, because both A and B are part of the
same solid object. From θB and rB, find SB, the distance moved by a point on its edge.
Next, look at gear C. Since gears B and C are meshed together, SC must equal SB. Find θC.
Continue on to D, E and F, finding the unknown angles and distances the same way as before.
The distance moved by a point on the edge of wheel F equals the displacement of the 25 g.
Experimentally check your answer for the distance moved by the 25 g. (Measure how far you pull it
down to make the 1 kg go up 2 cm.) Assume an uncertainty of ± 10% in both the calculated and
experimental values for s25. Comment on whether or not your values agree.
Part two
Purpose: To check the relationships vT = rω and aT = rα. A metal disk
is suspended from strings tied to its axle. You wind it up, then release
it. Observing its change in elevation, the number of revolutions it
turns, and the time to unwind lets you calculate the velocity and
acceleration of its center, and also its angular velocity and angular
acceleration. Measuring the radius around which the strings are wound
lets you calculate rω and rα, which you compare to v and a.
Procedure.
Distances from the lowest position make things simpler than using
distances from the floor: Subtract off z before recording h.
Wind the disk up about 15 or 20 revolutions, measuring this
distance, h. To measure θ, the angle turns as it unrolls, count
revolutions as you wind it up. This will be the same number as on
the way down, but easier to count. Wind it so that the string is
always wrapping around the axle itself, not on top of another layer
of string. Keep the disk centered between the strings as you wind to
keep it from rubbing them on the way down.
Release the disk, and measure the time, t, for it to reach the bottom. Do not let it rub on the strings.
Repeat, for a total of three trials, and average.
Measure r, the radius from which the string is unwinding. All of
your numbers are somewhat uncertain, but r is the major source
of uncertainty in this experiment. Is it just the radius of the axle?
The axle plus the string's thickness? Something in between? So,
using the micrometer, measure the radius of the bare axle for rmin,
and the axle plus the thickness of the string for rmax. Also record
the mass of the disk, M, from the tag attached near its edge, and
measure its radius, R. You will not use M or R today, but will
need them next week.
Compute the disk's average velocity and average angular velocity from their definitions. Compute
the quantity rω, using both the maximum and minimum possible r, and comment on whether rω
agrees with v.
Determine values for vo and vf, and use them to find the system's acceleration. Also, determine
values, ωo and ωf, and use them to find the system's angular acceleration. Compute the quantity rα,
and comment on whether it agrees with a.
PHY 121
Experiment 8: Rotation
Part One:
Wheel #1: rA =
Wheel #2: rC =
Wheel #3: rE =
CALCULATIONS:
SA = 2.0 cm
θA =
sB =
θC =
sD =
θE =
s25 = sF =
Experimental s25 =
rB = _____________
rD = _____________
rF = _____________
θ = _______________ ± 0
Part Two:
trial 1
z = ________________
trial 2
trial 3
h=
t=
axle diameter = _______________ string thickness = _______________
rmin= _______________
rmax= _______________
R = _______________
M = _______________
Calculations:
vav =
ωav =
r min ωav =
r max ωav =
vi =
vf =
a=
ωi =
ωf =
α=
rminα =
rmaxα =
average