Question

In: Physics

A bicyclist starts from rest and accelerates to 5 m/s in 20 s. The wheels of...

A bicyclist starts from rest and accelerates to 5 m/s in 20 s. The wheels of the bicycle have a diameter of 80 cm.

a) What is the angular velocity of the wheels at maximum speed?

b) What is the angular acceleration of the bicycle wheels during this time?

c) Find the number of revolutions the wheels make during this time.

d) Find the average angular velocity of the wheels between the start and finish.

Expert Solution

a) Let the maximum angular velocity of the wheel is .

Given that the maximum linear velocity of the wheel is v=5 m/s.

The radius of the wheel r=40 cm=0.40 m.

We know the angular velocity

The maximum linear velocity of the wheel is 12.5 rad/s.

b) Let the angular acceleration of the wheel during this time is .

The initial angular velocity of the wheel is =0 rad/s.

The time taken by the wheel is t=20 s.

We know the angular acceleration

The angular acceleration of the wheel during this time is 0.625 rad/s².

c) Let the total number of revolutions the wheel makes during this time is n.

We know

The number of revolutions the wheels make during this time is 19.89436789 revolutions or 19.90 revolutions.

d) Let the average angular velocity of the wheel during this time is .

We know average angular velocity

The average angular velocity of the wheel during this time is 6.25 rad/s.

genius_generous answered 2 years ago

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