When an object moves in a line, its position can be described with a single vari

Question

When an object moves in a line, its position can be described with a single variable usually called x. When an object rotates, we need a way to describe its angular position. This is done with the single variable, , (theta) which measures the angular distance the object rotates. Zero angle is usually taken along the positive r-axis and counterclockwise is taken as the positive angular direction. Although can be measured in degrees, there is another unit, (radians), that greatly simplifies calculations. This pre-lab is designed to help you become familiar with this new unit for measuring angular distance. Below is an equilateral triangle with sides of length r. To the right is the same triangle with an arc of a circle of radius r centered on point C. On the following page is a third drawing with a dot placed along the arc. This dot was positioned by measuring along the arc a distance r from the lower right corner. Note also there is a line connecting the dot to point C. Based on this construction, answer the questions on the following page.

Explanation / Answer

1) theta = arc/radius
if arc = radius, theta = 1 radian
the radian angle in degrees is = 57.32 degrees
2) 2*pi radians in complete circle
3) Face east, rotate CCW angle = 114.64 degrees, now you are facing 24.64 degrees counterclockwise of north
4) w = 1 rad/sec = 1 rotation / 2pi sec
2 rotation in 4pi secs = 6.28 s
5) w = 2pi/25 = 0.2512 rad/s
6) angle = 1/r
angle 1 = 1/0.1 = 10 rad
angle 2 = 1/0.05 = 20 rad

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