circular motion

Question

The angular speed of a rotating platform changes from ω₀ = 1.4 rad/s to ω = 8.2 rad/s at a constant rate as the platform moves through an angle Δθ = 8.5 radians. The platform has a radius of R = 16 cm.

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

b) calculate the tangential acceleration a_t in m/s² of a point on the surface of the platform at the outer edge.

c) calculate the final centripetal acceleration a_c in m/s² of a point at the outer edge of the platform

Answer 1

a) a = (ω² - ω₀²)/(2Δθ) = (8.2² - 1.4²)/(2·8.5) = 3.84 rad/s²

b) a_t = ar = 3.84·16 = 61.44 cm/s² = 0.6144 m/s²

c) a_c = ω²r = 8.2²·16 = 1075.84 cm/s² = 10.7584 m/s²