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This Exploration demonstrates that angles can be considered as if they were formed by the rotation of a line about a point, in much the same way that a spoke rotates round a bicycle wheel.
The applet below shows a bicycle wheel similar to the one on page 3-4 of your text.
Instructions
Click the button "Lab 3.1". A red dot is placed on the wheel so that the line joining the dot and the hub (centre) of the wheel makes an angle of 30o with the horizontal. If you press the key "P" on the keyboard of your computer, the point P will rotate counter-clockwise which is called the positive direction. Pressing "N" will make P move clockwise which is called the negative direction. Answer the questions below.
- Press "P" so that the point makes at least two rotations about the centre in the positive direction. Watch the size of the angle as P rotates.
(a) Through what angle has P moved by the time it gets to the top of the wheel the first time round?
(b) Through what angle has P moved by the time it gets to the bottom of the wheel the first time round?
(c) Through what angle has P moved by the time it gets to the top of the wheel the second time round?
- Press "N" so that the point makes at least two rotations about the centre in the negative direction. Watch the size of the angle as P rotates.
(a) Through what angle has P moved by the time it gets to the bottom of the wheel the first time round?
(b) Through what angle has P moved by the time it gets to the top of the wheel the first time round?
(c) Through what angle has P moved by the time it gets to the bottom of the wheel the second time time round?
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