Answer:
72.3 m/s²
Explanation:
Given:
ω₀ = 145.7 rpm × (2π rad/rev) × (1 min / 60 s) = 15.26 rad/s
ω = 177.1 rpm × (2π rad/rev) × (1 min / 60 s) = 18.55 rad/s
t = 7.1 s
Find: α
ω = αt + ω₀
18.55 = α (7.1) + 15.26
α = 0.463 rad/s²
After 2.3 s, the angular speed is:
ω = αt + ω₀
ω = (0.463) (2.3) + 15.26
ω = 16.32 rad/s
The tangential acceleration of a point on the edge is:
at = αr
at = (0.463 rad/s²) (0.543 m / 2)
at = 0.126 m/s²
The tangential speed of a point on the edge is:
v = ωr
v = (16.32 rad/s) (0.543 m / 2)
v = 4.43 m/s
The centripetal acceleration of a point on the edge is:
ac = v² / r
ac = (4.43 m/s)² / (0.543 m / 2)
ac = 72.3 m/s²
The total acceleration is:
a² = at² + ac²
a² = (0.126)² + (72.3)²
a = 72.3 m/s²
