Question

A bicyclist starting at rest produces a constant angular acceleration of 1.6 rad/s^2 for wheels that are 38 cm in radius. What is the bicycles linear acceleration? What is the angular speed of the wheels when the bicyclist reaches 11m/s? How many radians have the wheels turned through in that time? How far has the bicycle traveled?

Answer 1

Radius of the wheels = R = 38 cm = 0.38 m

Angular acceleration of the wheels = = 1.6 rad/s²

Linear acceleration of the bicycle = a

a = R

a = (1.6)(0.38)

a = 0.608 m/s²

Initial angular speed of the wheels = ₁ = 0 rad/s (At rest)

Speed reached by the bicyclist = V = 11 m/s

Angular speed of the wheels when the bicyclist reaches 11 m/s = ₂

₂ = V/R

₂ = 11/0.38

₂ = 28.947 rad/s

Angle through which the wheels have turned in this time =

₂² = ₁² + 2

(28.947)² = (0)² + (2)(1.6)

= 261.85 rad

Distance the bicycle has traveled = L

L = R

L = (0.38)(261.85)

L = 99.5 m

a) Bicycle's linear acceleration = 0.608 m/s²

b) Angular speed of the wheels when the bicyclist reaches 11 m/s = 28.947 rad/s

c) Angle through which the wheel has turned in this time = 261.85 rad

d) Distance the bicycle has traveled = 99.5 m