Converting Between Linear & Rotational Video Lessons

Concept

# Problem: A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 6.5 cm.The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R- 65 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.6s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.Randomized Variablesrp = 8.5 cmrw = 6.5 cmR = 65 cmt = 1.6 sPart (a) The pedal sprocket and the wheel sprocket have the same _________.a) Angular and tangential speedb) Radiusc) Tangential speed at their outer edges.d) Angular and tangential speedPart (b) Calculate the angular speed of the pedal sprocket ωp, in radians per second.Part (c) Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second. Part (d) Calculate the angular speed of the wheel sprocket ωw, in radians per second.Part (e) Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground. Part (f) If the cyclist wanted to travel at a speed of v2 = 5.5 m/s, how much time, in seconds, should elapse as the pedal makes one complete revolution?

###### FREE Expert Solution

Part a)

The wheel pocket and the pedal sprocket have different radio and different angular speeds.

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###### Problem Details

A bicyclist notes that the pedal sprocket has a radius of r= 8.5 cm while the wheel sprocket has a radius of r= 6.5 cm.The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R- 65 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.6s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.

Randomized Variables

rp = 8.5 cm
rw = 6.5 cm
R = 65 cm
t = 1.6 s

Part (a) The pedal sprocket and the wheel sprocket have the same _________.

a) Angular and tangential speed

c) Tangential speed at their outer edges.

d) Angular and tangential speed

Part (b) Calculate the angular speed of the pedal sprocket ωp, in radians per second.

Part (c) Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.

Part (d) Calculate the angular speed of the wheel sprocket ωw, in radians per second.

Part (e) Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.

Part (f) If the cyclist wanted to travel at a speed of v2 = 5.5 m/s, how much time, in seconds, should elapse as the pedal makes one complete revolution?