Question

A wheel rotates through an angle of 320° as it slows down from 78.0 rpm to 22.8 rpm. what is the magnitude of the average angular acceleration of the wheel?

Answer 1

The magnitude of the average angular acceleration of the wheel is 5.46 rad/s².

The magnitude of the average angular acceleration of the wheel is calculated as follows;

ωf² = ωi² + 2αΔθ

where;

ωf is the final angular speed
ωi is the initial angular speed
α is the angular acceleration
Δθ is the angular displacement
The angular displacement in radian is calculated as;

Δθ = (320 / 360) x 2π

Δθ = 5.59 rad

The magnitude of the average angular acceleration of the wheel is calculated as;

ωf² = ωi² + 2αΔθ

where;

ωf is the final angular speed = 78 rpm = 8.17 rad/s
ωi is the initial angular speed = 22.8 rpm = 2.39 rad/s
α = (ωf² - ωi²) / 2Δθ

α = (8.17² - 2.39²) / (2 x 5.59)

α = 5.46 rad/s²

Answer 2

The magnitude of the average angular acceleration of the wheel is 5.46 rad/s².

How to calculate the average angular acceleration?

The magnitude of the average angular acceleration of the wheel is calculated as follows;

ωf² = ωi² + 2αΔθ

where;

• ωf is the final angular speed
• ωi is the initial angular speed
• α is the angular acceleration
• Δθ is the angular displacement

The angular displacement in radian is calculated as;

Δθ = (320 / 360) x 2π

Δθ = 5.59 rad

The magnitude of the average angular acceleration of the wheel is calculated as;

ωf² = ωi² + 2αΔθ

where;

• ωf is the final angular speed = 78 rpm = 8.17 rad/s
• ωi is the initial angular speed = 22.8 rpm = 2.39 rad/s

α = (ωf² - ωi²) / 2Δθ

α = (8.17² - 2.39²) / (2 x 5.59)

α = 5.46 rad/s²