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# A bus slows down from 8.22 m/s to a stop in 13.3 s. Its wheels have a radius of 0.530 m. Find the initial angular speed of the wheels.

3 weeks ago

## Solution 1 Guest #7252952
3 weeks ago

The initial angular velocity of the bus wheel:

ω₀  ≈ 15.6 rad / s

Explanation:

Given:

V₀ = 8.22 m/s - Starting speed of the bus

V= 0 m/s - Final speed of the bus (the bus has stopped)

ω = 0 rad/c - Final angular velocity of the bus wheel

t = 13.3 s - Bus deceleration time

R = 0.530 m - Bus wheel radius

____________________

ω₀ - ?  - The initial angular speed of the wheels.

1) Bus linear acceleration module:

a = ( V₀ - V) / t = (8.22 - 0) / 13.3 ≈ 0.62 m/s²

2) Bus angular accelerations module:

ε = a / R = 0.62 / 0.530 ≈ 1.17 rad / s²

3) The initial angular velocity of the bus wheel:

ω₀ = ε·t  = 1.17·13.3 ≈ 15.6 rad / s

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