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revised 12-00

Appendix F. Problems in high-speed measurement

Problem 1. High-speed clocks

1. 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.
2. 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. 1. 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.
2. 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. 1. Measure the angle swept out by the clock hand and calculate the time interval between the flashes of light.
2. 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.
3. Measure the distance between the two images of the rip vertex. Then use the scale factor to convert to actual size.
4. Calculate the speed of the rip.
5. Estimate the uncertainties in your measurements of distance and time. Use them to estimate the uncertainty in the measurement of speed.
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