(Redirected from Tic Toc)

It's About Time is a physics and building event. It started in 1990 and ran as an event until 1998, but was brought back as an actual event for the 2009 tournament (Division C), continuing for the 2010 tournament season. After 4 years down, it returned as an official event for the 2015 season and was once again held for the 2016 season. The event was named Tic Toc as a division C event in 1990 and 1991.

Overview

This event tests student's knowledge of time and their skill in building a timekeeping device. The test portion covers general topics in the physics and history of time, with everything in between. The second portion involves a timekeeping device to determine the amount of time, between 10 and 300 seconds (5 minutes), with a precision of 0.1 seconds.

Teams may bring one 3-ring binder of any size and calculators, though the calculator(s) may only be used during the written portion of the test, not during the time trials. Stop watches, scales, etc. are allowed to calibrate the device before the trials begin, but will not be allowed during the actual test.

Time Trials and Time Devices

Students will use their pre-built devices to determine the time intervals of three trials. More points are deducted per 0.1 second error in Trial 1 and is lessened in the later trials.

1. Trial 1 will be from 10-90 seconds
2. Trial 2 will be from 90-300 seconds
3. Trial 3 will be from 10-300 seconds

Constrictions

• The timekeeping device may not use electricity or chemical reactions.
• The device's initial size cannot exceed 80cm x 80cm x 80cm.
• The device must be impounded.

Testing

There are sound files for every possible time trial located at the national site (see links below). However it should be noted that problems may arise when using the files on Microsoft Windows Media Player, so it would be best when testing to use another program.

During the event all clocks will be covered up in the room to prevent cheating. Remember that the use of cellphones, watches, and other similar devices are prohibited during the test.

Devices

Your best bet would be to build a water or pendulum clock, however if building a water, sand, or clock that uses moving parts (such as marbles), make sure that all spillage is contained. Points can be deducted if water or sand are spilled on the table or floor, or if something drops.

For pendulum clocks, the most important factor is the length of the pendulum, not the weight at the end (though there should be sufficient mass at the end of the pendulum). Pendulum clocks will also need to last five minutes without becoming too inefficient. Sand clocks are also an option, however there are too many variables to consider for it to be a viable clock. The sand may clog the hole, and moisture would also provide an obstacle.

Another popular clock was the spring-mass oscillator. As with the pendulum clocks, it needs to be able to oscillate for over five minutes to be able to work. The most important factor determining the period is the mass and the spring constant.

Written Test

The written test will constitute 50% of the final grade, the other half being the results from the time trial portion. Students may bring with them one 3-ring binder of any size to help them with the test. However it is a good idea for teams to know as much of the information possible as time will be short and with only 20-30 minutes to take the test. Teammates will be strapped for time, so knowing as much as possible without having to search through a binder, along with splitting the test up should allow the longer tests to be completed.

Students should be prepared for math problems, history questions, and anything and everything that has to do with time. Topics such as horology (the study of timekeeping), space-time, atomic clocks, and even old phrases and proverbs that deal with time could be in the test.

Be prepared for anything, as any physics questions having to do with measuring time may show up. The test will not necessarily provide any equations, so it is a good idea to bring a formula sheet.

List of Topics

This event has a large range of questions that stretch across many disciplines of science. Common topics include

• Geography, mainly latitude and longitude, as well as time zones and differences between locations
• Motion equations
• Constant acceleration equations like $x = x_0 + v_0 t + \frac{1}{2} at^2$
• Rotation
• Relativistic time dilation and the Lorentz factor
• Geological time questions - what happened in which geological period
• Simple harmonic motion, which usually involves finding the periods of
• Pendulums
• Mass on a spring
• Astronomy
• Knowing the rotation and orbital periods of the eight planets
• Finding orbital period using Kepler's third law
• History - including history of clock making and key dates in horology
• Calendars
• Gregorian calendar, Julian calendar, leap years
• Day of week
• Calendars of other cultures, such as the Mayan calendar.
• Time units, both the common ones and some obscure ones
• Time standards
• Some factoid type questions

Some less likely possibilities include

• Calculations
• Kinetics (from chemistry)
• Newton's law of cooling
• Complicated pendulums where the moment of inertia has to be calculated first
• Complicated combinations of multiple masses, springs, and walls
• Linear drag
• Length of a day given the date and the latitude
• Electricity and magnetism
• I = q/t
• Cyclotron frequency
• RC, RL, LC circuits
• Doppler effect
• Other
• Calculating Julian Date, e.g., 2457396.
• Famous clocks

The questions can be in any format, multiple choice, short answer, true-or-false, long answer, mathematical (be sure to show work), plotting, among others.

Sample Questions

• If it is 10:30 p.m. EST, what time is it in New Zealand?
• From where does the phrase, "a stitch in time saves nine" originate?
• How long ago was the planet Earth formed?
• What is the difference between a sidereal and solar day?
• The abbreviation NIST stands for what?
• On what is the second based?
• How many leap seconds have been implemented?
• On which day of the week will the next February 29 occur?
• How long is a year on the planet Jupiter?
• What is today's Julian date?

Calendars

There are multiple types of calendars depending on which astronomical bodies are used to keep time. Some calendars are purely lunar, while others attempt to use both the sun and the moon, others are purely solar, and there are many variations on this that have been used in various places, occassions, and times.

Even solar-based calendars have a problem: the length of a day (governed by primarily the rotation of the Earth) and the length of a year (governed by the orbit of the Earth around the sun) are mostly independent astronomical quantities that do not have a whole number ratio. In fact, a year is approximate 365.242 days. As such, if a calendar attempted to have an exact number of days in every year (eg. 365 days), then the calendar would shift with respect to the movement of the sun in the sky (eg. equinoxes and solstices would shift weeks after just one century).

One of the most prominent Western solutions to this problem was called the Julian calendar, named after Julius Caesar, during whose reign it was introduced. It introduced a leap-year every 4 years to correct this discreptancy, as well as introducing the modern 12 months with the same lengths. However, 365.25 days per year is too long, drifting by approximately 3 days every 400 years. As such, by the 1500s, the calendar had drifted by over a week.

In 1582 the Gregorian calendar was introduced, named after Pope Gregory XIII. Instead of having a leapyear every 4 years, it cut out 3 leap-years every 400 years, such that years divisible by 100 are only leap-years if they are also divisible by 400. (Eg. 1600 and 2000 were leap-years, but not 1700, 1800, or 1900). The adoption of the calendar also involved skipping several days in 1582. The calendar was adopted by some countries quickly, but others such as Russia, retained the Julian calendar into the early 20th century. This creates ambiguity in historical dates, so they are sometimes indicated as O.S or N.S. (Old Style and New Style respectively).

Calculating the day of the week for Gregorian calendar dates

The following method is based on the Doomsday rule as invented by the mathematician John Conway with a small variation in calculation.

Math background

Calendar calculations find useful the concept of a modulus. A modulus may be informally thought of as the "remainder" of a division. They are formed by looping the integers around, so that in mod n, (n-1)+1=0=n=2n=3n=4n=5n... (NB: in formal math, the equality sign is not typically used in this manner with modulus, but a three lined congruence symbol)

So as an example in mod 7:
24mod7 = 24-3(7) = 24-21 = 3
47mod7 = 47-6(7) = 47-42 = 5

Note that in the above calculations, 24mod7 can also equal 10, 17, 24, et cetera, since 24-2(7) = 10, and so on.

Mod 4 is also useful for leap-years, since if x mod 4 is 0, then x is (usually) a leap year:
2002 mod 4= 2002-500(4)=2, thus not a leap-year

Convention

To reduce the calculations to integer arithmetic, the days of the week are represented by integers in mod 7.

Days of Week
Day Number
Sunday 0
Monday 1
Tuesday 2
Wednesday 3
Thursday 4
Friday 5
Saturday 6

Some Mnemonics to remember it are Monday="One-day" and Tuesday="Two-day".

For the purpose of this calculation, centuries are considered to begin on '00 years.

Method

Caveat: This method is intended for years ce/ad, a variation will be needed for years bce/bc.

1. Determine the anchor-day for the century.

These alternate in a 400 year-cycle with a pattern of 5,3,2,0,5,3,2,0,... the 1900s have an anchor-day of 3 (Wednesday) and the 2000s of 2 (Tuesday). The remaining centuries can be extrapolated from this pattern. The anchor-day for a century also corresponds to the doomsday for the '00 year of that same century, so if this is the case, you can skip step 2.

2. Determine the doomsday for the year.

Take only the last two digits of the year. If the original year was odd, add 11. Next, divide the year by 2, regardless of whether it was odd or not. If the year is odd after the division, add 11 to make it even once more. Take this remaining number mod 7, and subtract this result from 7. Finally, add the anchor-day from step 2. If the result is 7 or greater, subtract 7. This will be your doomsday for the year.

Examples:
2037->(cut out year) 37->(add 11) 48->(divide by 2) 24->(mod 7) 3->(subtract from 7) 4->(add 2 for anchor-day) 6
1938->(cut out year) 38->(divide by 2) 19->(add 11) 30->(mod 7) 2->(subtract from 7) 5->(add 3 for anchor-day) 8->(subtract 7) 1
1848->(cut out year) 48->(divide by 2) 24->(mod 7) 3->(subtract from 7) 4->(add 5 for anchor-day) 9->(subtract 7) 2

(Alternately, you can look it up in a table)

3. Determine if leap-year

This step can be skipped if the desired month is not January or February. Otherwise, see above for the detailed rules on leap-years for the Gregorian calendar.

4. Find a nearby date that falls on doomsday.

Some basic memorable dates: (Month/year)
4/4, 6/6, 8/8, 10/10, 12/12
5/9, 9/5, 7/11, 11/7
3/14 (Pi day!)
The last day in February (28th if non-year, else 29th)
January 3rd if non-leap-year, else January 4th.

You can also memorize dates a multiple of 7 days away to keep numbers smaller in step 5.

5. Calculate day of the week

Calculate the difference between the desired date and the nearby date and add or subtract it from the doomsday. Use mod 7 to bring the result into the range of 0-6 to get the day of the week.

Example: January 13th, 1848
In the third example of step 2, we calculated the doomsday of 1848 as 2. Since it is January, pay extra attention to the fact that it is a leap year (divisible by 4 and not divisible by 100). Since January 4th is near the 13th and is a doomsday for a leap-year, we calculate that the 13th is 9 days after the 4th. By adding 9 to the doomsday of 2, and then using mod 7, we get (9+2)mod7=11mod7=4. Therefore January 13th, 1848 was a Thursday.

In the beginning the algorithm may seem long and complex, but with practice it can become very fast.