A wheel of radius 24 ft is rotating 11 RPM counterclockwise

A wheel of radius 24 ft. is rotating 11 RPM counterclockwise. Considering a point on the rim of the rotating wheel, what is the angular speed co in rad/sec and the linear speed v in ft/sec? omega = rad/sec V= ft/sec A wheel of radius 6 in. is rotating 45 degree/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec? v = in/sec omega= rpm omega= rad/sec You are standing on the equator of the earth (radius 3960 miles). What is your linear and angular speed? V= mph omega= rad/hr An auto tire has radius 12 inches. If you are driving 60 mph, what is the angular speed in rad/sec and the angular speed in RPM? Omega= rad/sec omega= rpm

Solution

a) 11rpm*(24*2*pi)ft/rotation*(1 min)/60sec = 27.65 ft/sec

This is the linear speed.

Angular speed is:
w= v/r
w= 27.65/24 =1.15 rad/sec

b) 45 degree/sec = pi/4 rad/sec

So, angular speed = w = pi/4 rad/sec = 15 pi rad/min = 7.5 RPM

Linear speed = v = w*r = (pi/4)*6 in/sec

c)  One full rotation = 2*pi radians in 24 hours
24 hours = 86,400 sec
roughly 7 x10^-5 radians / sec

Point on Equator moves 2*pi*radius in 24 hours
24,881 miles per day
Roughly 1037 miles per hour.

d) 60 miles/hr * 5280 ft/mile * 1hr/60min = 5280 ft/min
5280 ft/min * 12in/ft * 1min/60sec = 1056 in/sec

v = r
= v/r = (1056 in/sec) / (12 in/rad) = 88 rad/sec

1 revolution = 2r = 2 * 1ft = 2 ft

= (5280 ft/min) / (2 ft/revolution) = 840.3 RPM