Grades 1-2 Video Solutions 2021-video 2021 1-2/20

Video Transcription

Problem number 20. The picture shows two gears, each with a black tooth. Where will the black teeth be after the small gear has made one full turn? A, B, C, D, or E?  With gears, when one of them moves, the teeth kind of catch against each other, so each gear moves the same number of teeth. However, they move in opposite directions.  The first thing to do is to count the number of teeth on each gear. The small gear has 1, 2, 3, 4, 5, 6, 7, 8. Eight teeth.  And the larger gear has 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. 16 teeth.  When the small gear makes one full turn, it will move by 8 teeth, with the black tooth returning to where it started. And the large gear will also move by 8 teeth.  Because the big gear has 16 teeth, when it moves by 8 teeth, it moves halfway around. It will move in this direction.  We just need to find which tooth is halfway across from where the black tooth started. So we can just draw a line here, and the tooth is right here.  We could also count 1, 2, 3, 4, 5, 6, 7, 8. So the black tooth will be right here, on the bottom.  This situation is shown in answer C. So the answer is C.

Video Summary

The problem involves determining the position of black teeth on two interconnected gears after one full turn of the smaller gear. The small gear has 8 teeth, and the larger gear has 16 teeth. When the small gear completes one full rotation, moving its black tooth back to the starting position, the larger gear moves 8 teeth in the opposite direction due to their gear mechanism. This displacement is half the number of the larger gear's teeth, meaning the black tooth on the larger gear ends up directly opposite its starting point. Therefore, the correct answer, where the black tooth aligns, is position C.

Keywords

gear mechanism

tooth position

gear rotation

gear alignment

black tooth