Question

The angular speed of a rotating platform changes from ω0 = 3.8 rad/s to ω = 7.2 rad/s at a constant rate as the platform moves through an angle Δθ = 5.5 radians. The platform has a radius of R = 36 cm.

a) calculate the angular acceleration of the platform in rad/s²

Answer 1

The angular acceleration of the platform is found to be 3.4 rad/s² by using the kinematic equation for rotational motion.

Step-by-step explanation:

To calculate the angular acceleration of the platform, we can use the kinematic equation for rotational motion:

α = (ω - ω_0) / Δt

However, we first need to find the time Δt it takes for the platform to go through the angle Δθ at a constant angular acceleration. Since we know the initial and final angular velocities and the angle, we can use the following equation:

ω^2 = ω_0^2 + 2αΔθ

Rearranging the equation to solve for α, we get:

α = (ω^2 - ω_0^2) / (2Δθ)

Substituting in the provided values:

α = (7.2^2 - 3.8^2) / (2 × 5.5) rad/s²

α = (51.84 - 14.44) / 11 rad/s²

α = 37.4 / 11 rad/s²

α = 3.4 rad/s²

Therefore, the angular acceleration of the platform is 3.4 rad/s².