Answer:
Explanation:
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
Answer:
(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 = 2Ф/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
