Through how many degrees does the hour hand in a clock move as the time changes from 3 hours and 12 minutes to 6 hours?

To find the degrees moved by the hour hand, we calculate the total time elapsed between 3:12 and 6:00. The duration is 2 hours and 48 minutes. In a standard 12-hour clock, the hour hand completes a full 360° rotation in 12 hours, meaning it moves 30° per hour [1]. Furthermore, since there are 60 minutes in an hour, the hour hand moves at a rate of 0.5° per minute (30° / 60). For the 2-hour period, the hand moves 60° (2 × 30°). For the remaining 48 minutes, it moves 24° (48 × 0.5°). Adding these together, the total movement is 60° + 24° = 84°. This calculation follows the standard mechanical principle where the hour hand moves continuously rather than in discrete hourly jumps.

Sources

1. [1] Certificate Physical and Human Geography , GC Leong (Oxford University press 3rd ed.) > Chapter 2: The Earth's Crust > Longitude and Time > p. 11