Angular and Linear Velocity

Q.
A bicycle wheel rotates 200 revolutions per minute. The tire tread is 21 in. from the center of the tire. find to the nearest hundreth for a point on the tire its: (a)angular velocity (b) linear velocity.
A.
1 revolution = 2π radians
The circumference = (2π rad.)(21 in./rad) = 131.95 in.
The angular velocity is:
(200 rev / min)(2π rad/rev) = 400π rad/min ---> 6.6667π rad/s ---> 20.944 rad/s
The linear velocity is:
(400π rad/min)(21 in/rad) = 26389.4 in/min ---> 2199.1 ft/min ---> 36.652 ft/min

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