Angular velocity:

$\overline{){\mathbf{\omega}}{\mathbf{=}}\frac{\mathbf{\u2206}\mathbf{\theta}}{\mathbf{\u2206}\mathbf{T}}}$

Tangential speed:

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega}}}$

**Part (a) **

Radius is different. Chian speed (Tangential speed) is the same for both. Angular velocity is different because of the difference in radius.

A bicyclist notes that the pedal sprocket has a radius of r_{p }= 11 cm while the wheel sprocket has a radius of r_{w} = 5.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 68 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.7s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.

Randomized Variables

r_{p }= 11 cm

r_{w} = 5.5 cm

R = 68 cm

t = 1.7s

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

a) Angular and tangential speed

b) Centripetal acceleration

c) Tangential speed at their outer edges

d) Radius

Part (b) Calculate the angular speed of the pedal sprocket w_{p}, in radians per second.

Part (c) Calculate the linear speed of the outer edge of the pedal sprocket v_{p} in centimeters per second.

Part (d) Calculate the angular speed of the wheel sprocket ω _{w}_{ }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 v_{2 }= 4.5 m/s, how much time, in seconds should elapse as the pedal makes one complete revolution?