Sample Response: I am asked to find linear velocity and am given revolutions per minute. Since there are 2pi
radians in 1 revolution, I can convert rpm to radians per
minute by multiplying by 2pi. The angular displacement
is 2opi radians, so the angular velocity is 2opi radians per
minute. Next, I know that linear velocity is equal to
angular velocity times the radius. Using 3.14 for pi and
multiplying 20pi by 2 feet, I approximate the linear
velocity as 125.6 feet per minute. This linear velocity of
125.6 divided by the radius of 2 feet does give me 62.8
radians per minute. Since 62.8 radians per minute is
about 2opi radians per minute, this checks. Linear
velocity is arc length over time. I can see if this result is
reasonable by finding the arc length. The circumference
of the wheel is 4pi or about 12.5 feet. If a point on the
edge of the wheel can travel about 12.5 feet in 1
revolution, then it travels about 125 feet in 10 revolutions.
It is reasonable for the linear velocity to be about 125.6