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 2πr (π 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 2π radians (or 6.28 radians) is the same as 360°.

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 2πr (π 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 2π radians (or 6.28 radians) is the same as 360°. 
a.) What is a 82.9° angle in terms of radians? (Normally you would enter units of rad, but in this case do not enter units.) 
b.) If a wheel turns around 6.00 complete rotations, what would the angular displacement of that wheel be in radians? (Enter units of rad)

Henry · Answer

a. 6.28/360o = x/82.9o, x = 82.9 * 6.28/360 = 1.45 Radians. b. 6.28rad/rev * 6revs =