circular motion

Question

At its lowest setting a centrifuge rotates with an angular speed of ω₁ = 350 rad/s. When it is switched to the next higher setting it takes t = 12.5 s to uniformly accelerate to its final angular speed ω₂ = 750 rad/s.

a) calculate the angular acceleration of the centrifuge a₁ in rad/s² over the time interval t.

b) calculate the total angular displacement (in radians) of the centrifuge, delta θ, as it accelerates from the initial to the final speed

Answer 1

The equations for rotational motion are analogous to those of linear motion.

a. Angular acceleration α = (ω_final - ω_initial) / t = 750 rad/sec - 350 rad/s / 12.5 s = 32.0 rad / s²

b. θ = ω₀ t + 1/2 α t² = 350 rad/sec x 12.5 s + 1/2 x 32.0 rad/s² x 12.5s² = 688 radians