Question

The angular speed of a rotating platform changes from a 3.8 rad/s to o=64 rad/s at a constant rate as the platform moves through an angle A-9.5 radians. The platform has a radius of R 36 cm.

Randomized Variables
w0=3.8 rad/s
w=6.4 rad/s
∆θ=A89.5 radians
R=36 cm
Calculate the angular acceleration of the platform a in rad/s².
α = ___

Answer 1

The angular acceleration of the platform is calculated using the formula that relates angular acceleration to the change in angular velocity and the angle rotated. Using the given values, the angular acceleration is found to be approximately 1.3958 rad/s².

Step-by-step explanation:

To calculate the angular acceleration (α) of the rotating platform, we can use the formula that relates angular acceleration to the change in angular velocity (ω) and the angle (Δθ) through which the platform has rotated:

α = (ω² - ω₀²) / (2Δθ)

Where:

• α is the angular acceleration in rad/s²,
• ω is the final angular velocity in rad/s (6.4 rad/s),
• ω₀ is the initial angular velocity in rad/s (3.8 rad/s), and
• Δθ is the angle in radians through which the platform has rotated (9.5 radians).

Plugging the given values into the formula, we get:

α = (6.4² - 3.8²) / (2 × 9.5)

α = (40.96 - 14.44) / 19

α = 26.52 / 19

α = 1.3958 rad/s²

The angular acceleration of the platform is approximately 1.3958 rad/s².