How to Calculate Time and Uncertainty for Rotating Pulsars

[scmejla]

Hello, perhaps you could help with a problem.

Suppose a pulsar rotates once every 1.400 806 448 872 75 + or - 5 ms, where the trailing + or - 5 indicates the uncertainty in the last decimal place (it does not mean + or - 5ms).

a. How many times does the pulsar rotate in 30.0 days?
I solved this one, 30days(60s/min)(60min/hr)(24hr/day) = 1.85(10^9)

b. How much time does the pulsar take to rotate 2.0(10^6) times?
(Give your answer to at least 4 decimal places.)

c. What is the associated uncertainty of this time?

It's these last two that are giving me issues, for b. I figured you just multiply the amount of rotations by the time it takes to rotate, I came up with 2801.61 s but according to webassign is wrong. I even stuffed it with 2 zeros to go out 4 decimal places. I'm just not sure about c, though I need the answer to b. to start.

 

[HallsofIvy]

Hello, perhaps you could help with a problem.

Suppose a pulsar rotates once every 1.400 806 448 872 75 + or - 5 ms, where the trailing + or - 5 indicates the uncertainty in the last decimal place (it does not mean + or - 5ms).

a. How many times does the pulsar rotate in 30.0 days?
I solved this one, 30days(60s/min)(60min/hr)(24hr/day) = 1.85(10^9)

Your notation is misleading! (30)(60)(60)(24)= 2592000. Then you multiplied by 1000 ms/s and divided by 1.400 806 448 872 75 ms.

b. How much time does the pulsar take to rotate 2.0(10^6) times?
(Give your answer to at least 4 decimal places.)

c. What is the associated uncertainty of this time?

It's these last two that are giving me issues, for b. I figured you just multiply the amount of rotations by the time it takes to rotate, I came up with 2801.61 s but according to webassign is wrong. I even stuffed it with 2 zeros to go out 4 decimal places.

What do you mean "stuffed it with 2 zeros? 2(10^6)= 2000000 and since you are multiplying by approximately 1.4, you should get about 2800000.
I get 2801612.8977455.

I'm just not sure about c, though I need the answer to b. to start.

1.400 806 448 872 75 + or - 5 ms, could be as large as 1.400 806 448 872 75 +5 = 1.400 806 448 872 80 ms or a small as 1.400 806 448 872 75 -5 = 1.400 806 448 872 70 ms. Do your calculation using each of these, then find the average of the two extremes. The uncertainty will be that average + or - something.

 

[scmejla]

Thank you for your help, you've led me to the correct answer. It is 2801.6128977455, you must have left out the (ms) or 10^-3 when multiplying. My calculator was only set up to display 6 digits. Thanx again.