While riding a multispeed bicycle, the rider can select the radius of the rear sprocket that is fixed to the rear axle. The front sprocket of a bicycle has radius 12.0 cm. If the angular speed of the front sprocket is 0.600 rev/s, what is the radius of the rear sprocket for which the tangential speed of a point on the rim of the rear wheel will be 5.00 m/s? The rear wheel has radius 0.330 m.

Solution 71P Step 1 of 5: The front sprocket of bicycle has radius r =12fcm rotating with frequency f =0.6 revfs. The tangential speed of the rim of rear wheel is v=5 m/s with rear wheel radius r = w 0.330 m. We need to calculate the radius of the rear sprocket to achieve given tangential speed. Given data, front sprocket radius r =f2 cm front sprocket frequency f =0f6 rev/s rear wheel rim speed v=5 m/s rear wheel radius r =w0.330 m To find, Angular speed of rear wheel , = Frequency of the rear wheel, f = r Radius of the rear sprocket, r= Step 2 of 5: To calculate the angular speed of rear wheel, Relation between tangential speed(v) and angular speed() = v rw Where r iw radius of rear rim moving with tangential speed v. Substituting v=5 m/s and r = w.330 m 5 m/s = 0.330 m = 15.15 rev/s Step 3 of 5: To calculate the angular frequency of rear rim, From the fundamental relation of frequency, fr= 2 Substituting = 15.15 rev/s 15.15 rev/s fr= 2 f =2.41 rev r