Appendix F. Problems in high-speed measurement
Problem 1. High-speed clocks
- Clocks with rotating hands measure time in terms of the angle swept out by the hand during the time interval. Representing the angle as q and the period of the hand as T, write an equation for the time interval, Dt, in terms of q and T.
- The photograph below shows two rotating discs, A and B. Although each disc has a single hand, two images of the hand are seen because the discs were lit by sequential bursts of light from two flash units. The frequency of disc B was measured with a stroboscope and found to be 50.5 rotations per second.
- Determine the time interval between the bursts of light. Also estimate the uncertainty in your result, based on the accuracy and precision of your measurement of angle.
- Determine the period of disc A.
Problem 2. Speed of a balloon rip
The figure below shows a double-exposure of a balloon rip taken according to the method of Activity 16. The frequency of the clock was 51.7 rotations per second, and the diameter of the disc was 0.105 m.
- Measure the angle swept out by the clock hand and calculate the time interval between the flashes of light.
- Measure the diameter of the clock disc on the photograph and calculate a scale factor to be used in converting distances measured on the photograph to actual size.
- Measure the distance between the two images of the rip vertex. Then use the scale factor to convert to actual size.
- Calculate the speed of the rip.
- Estimate the uncertainties in your measurements of distance and time. Use them to estimate the uncertainty in the measurement of speed.