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/s^{2}
?

rad/s^{2}

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

======================================

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