We can measure angles in degrees or radians. When studying angular motion, we wi

Question

We can measure angles in degrees or radians. When studying angular motion, we will tend to use radians. If you are looking at a portion of a circle, the angle in radians can be calculated by dividing the arc length by the radius of the circle. The arc length for a complete circle is just the circumference, which can be calculated as 2r ( represents the greek letter pi, which numerically is approximately 3.1416). A complete circle also represents an angle of 360°. From this we can get the conversion factor that 2 radians (or 6.28 radians) is the same as 360°. What is a 107° angle in terms of radians? (Normally you would enter units of rad, but in this case do not enter units.) Tries 0/10 If a wheel turns around 8.00 complete rotations, what would the angular displacement of that wheel be in radians? (Enter units of rad)

Explanation / Answer

convert the angle from degrees to radians

107° = (107°)(2/360°)

=1.87 rad

8 complete rotiation = 8( 2 )

= 16 rad

= 50.26 rad

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