Question

The angular speed of a rotating platform changes from ω₀=2.8 rad/s to ω=8.8 rad/s at a constant rate as the platform moves through an angle Δθ=5.5 radians. The platform has a radius of R = 28 cm.

(a) Calculate the angular acceleration of the platform.

Answer 1

The angular acceleration of the platform is calculated using the change in angular velocity and the angular displacement, using the kinematic equation for rotational motion. The angular acceleration of the platform is approximately 6.327273 rad/s².

Step-by-step explanation:

To calculate the angular acceleration of the platform, we can use one of the equations of rotational motion that relates angular displacement (Δθ), initial angular velocity (ω₀), final angular velocity (ω), and angular acceleration (α). Specifically, we will use the following kinematic equation for rotational motion:

ω² = ω₀² + 2αΔθ

where
ω is the final angular velocity,
ω₀ is the initial angular velocity,
α is the angular acceleration, and
Δθ is the angular displacement.

The task is to find the angular acceleration (α). We are given:
ω₀ = 2.8 rad/s (initial angular velocity),
ω = 8.8 rad/s (final angular velocity), and
Δθ = 5.5 radians (angular displacement).

We can rearrange the equation to solve for the angular acceleration (α):

α = (ω² - ω₀²) / (2Δθ)

Let's plug in the given values and do the calculation:

α = ((8.8)^2 - (2.8)^2) / (2 * 5.5)

Calculating the squared velocities first:

ω² = (8.8)^2 = 77.44 rad²/s²
ω₀² = (2.8)^2 = 7.84 rad²/s²

Substituting these values into the equation for α gives us:

α = (77.44 - 7.84) / (2 * 5.5)
α = 69.6 / 11
α = 6.327273 rad/s² (approximately)

The angular acceleration of the platform is approximately 6.327273 rad/s².