A high-wheel antique bicycle has a large front wheel with the foot-powered crank mounted on its axle and a small rear wheel turning independently of the front wheel; there is no chain connecting the wheels. The radius of the front wheel is 65.5 cm, and the radius of the rear wheel is 22.0 cm. Your modem bike has a wheel diameter of 66.0 cm (26 inches) and front and rear sprockets with radii of 11.0 cm and 5.5 cm, respectively. The rear sprocket is rigidly attached to the axle of the rear wheel. You ride your modem bike and turn the front sprocket at 1.00 rev/so The wheels of both bikes roll along the ground without slipping.
(a) What is your linear speed when you ride your modem bike? (b) At what rate must you turn the crank of the antique bike in order to travel at the same speed as in part (a)?
(c) What then is the angular speed (in rev/s) of the small rear wheel of the antique bike?