Question

A cyclist starts from rest and pedals such that the wheels of his bike have a constant angular acceleration. After 19 s, the wheels have made 40 revolutions.

If the radius of the wheel is 30 cm, how far did the bike travel?
m

Tries 0/2

How many radians has the wheel rotated after 19 s?

rad

Tries 0/2

What is the angular velocity after 19 s?

rad/s

You have the radians turned, and time. You'll probably want to find the average angular velocity first, and then final angular velocity.

Incorrect.

Tries 1/2

Previous Tries

What is the angular acceleration in rad/s2?

rad/s²

Answer 1

Radius of the wheel = R = 30 cm = 0.3 m

Number of revolutions made by the wheel in 19 sec = N = 40 rev

Time period = T = 19 sec

Distance traveled by the bike in 19 sec = L

In one revolution the wheel will travel a distance equal to the circumference of the wheel that is '2R'.

L = 75.4 m

Angle through which the wheels have rotated in 19 sec =

= 251.3 rad

Average angular velocity of the wheels =

= 13.226 rad/s

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

Angular velocity of the wheels after 19 sec = ₂

₂ = 26.45 rad/s

Angular acceleration of the wheels =

= 1.39 rad/s²

a) Distance traveled by the bike = 75.4 m

b) Angle through which the wheels rotated = 251.3 rad

c) Angular velocity of the wheels after 19 sec = 26.45 rad/s

d) Angular acceleration of the wheels = 1.39 rad/s²