circular motion

Question

this problem confused me

A disk with an initial angular velocity ω₀ = 3.5 rad/s experiences a constant angular acceleration of α = 8.5 rad/s² for a time period t = 25 s. Please answer the following questions.

ω₀ = 3.5 rad/s

α = 8.5 rad/s²

t = 25 s

a) write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters

b) calculate the magnitude of the angular velocity of the disk in rad/s at time t.

c) write an expression for the magnitude of the angular displacement Θ traveled by a point on the disc during the angular acceleration described in terms of given parameters. assume the point starts at an angular displacement of 0 radians.

d) calculate the magnitude of the angular displacement in radians traveled by a point on the disc during acceleration described.

Answer 1

Analogous to projectile motion in the presence of constant gravitational acceleration, the angular displacement under constant angular acceleration is given by

θ = θ₀ + ω₀t + 0.5αt²

The time derivative of this expression gives

a) ω = ω₀ + αt = 3.5 + 8.5t

b) ω = 3.5 + 8.5(25) = 216 rad/s

c) θ = 3.5t + 4.25t² (expression above with θ₀ = 0)

d) θ = 3.5(25) + 4.25(25)² = 2743.75 rad