Question

A cyclist starts from rest and pedals such that the wheels of his bike have a constant angular acceleration.
After 12 s, the wheels have made 40 rev.

What is the angular velocity of the wheels after 12 s in rad/s ?

rad/s

Tries 0/3

What is the angular acceleration of the wheels in rad/s² ?

rad/s²

Tries 0/3

If the radius of the wheel is 33 cm, and the wheel rolls without slipping, how far has the cyclist (in m) traveled in 12 s?

m

Tries 0/3

Answer 1

θ is the angulaar displacement
α is the angular acceleration.
ωis the angular velocity
N is the frequency.
1 revolution = 2π radian.
--------------------------------------...



θ = 1/2 *α *t^2
2π *40 = 1/2 *α *12^2
α= 4*3.14*40/ 12^2= 3.5 rad/s^2
---------------------------------
ω2 = α*t = 3.5*12 = 42 rad /s

======================
Angle traversed = 2π *40 Radian
s = rθ = 0.33*2π *40= 83.m
===============================

Angular acceleration of the wheels = 3.5 rad/s^2
Angular velocity of the wheels after 12.0 s= 42 rad /s
Distance traveled in 12.0 s by the cyclist = 83.m
======================================

hope this helps you. please thumbs up now?