Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.00 s, it rotates 14.8 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity

(a) 1.184 rad/s²

(b) 2.96 rad/s

Explanation:

(a)

Using,

Ф = ω₀t + 1/2αt² ... Equation 1

Where Ф = angular distance, ω₀ = initial angular velocity, α = angular acceleration, t = time.

Since the disk starts from rest, ω₀ = 0 rad/s,

Therefore,

Ф = 1/2αt²

make α the subject of the equation

α = 2 Ф/t² ... Equation 2

Given: Ф = 14.8 rad, t = 5.0 s

Substitute into equation 2

α = 2*14.8/5²

α = 29.6/25

α = 1.184 rad/s²

(b)

Using,

Ф = ω't ... Equation 3

Where ω' = Average angular velocity.

Then,

make ω' the subject of the equation

ω' = Ф/t ... Equation 4

Given: Ф = 14.8 rad, t = 5.0 s

Substitute into equation 4

ω' = 14.8/5

ω' = 2.96 rad/s

Given:

Initial θ = 0 rad (from rest)

Final θ = 14.3 rad

Time, t = 5 s

B.

Angular velocity, w = dθ / dt

= (14.3 - 0) / 5

= 2.86 rad/s

A.

Acceleration, ao = dw/dt

Initial angular velocity, wi = 0 rad/s (from rest)

Final angular velocity, wf = 2.86 rad/s

a = (2.86 - 0) / 5

= 0.572 rad/s^2