Answer:
0.11 rev
Step-by-step explanation:
There are two possible approaches:
- First find the angular acceleration of wheel C, then find the angular displacement.
- Or, find the final angular velocity of wheel A, then the angular displacement of wheel A, then finally the angular displacement of wheel C.
The first method is only two steps, so let's use that.
Both wheels have the same tangential acceleration:
aA = aC
αA rA = αC rC
(2.0 rad/s²) (1.0 m) = αC (2.5 m)
αC = 0.8 rad/s²
Given for wheel C:
ω₀ = 0 rad/s
ω = 10 rev/min × (1 min / 60 s) × (2π rad/rev) = π/3 rad/s
α = 0.8 rad/s²
Find: Δθ
ω² = ω₀² + 2αΔθ
(π/3)² = (0)² + 2 (0.8) Δθ
Δθ = 0.685 rad
Convert to revolutions:
Δθ = 0.685 rad × (1 rev / 2π rad)
Δθ = 0.109 rev
Rounded to two significant figures, wheel C will have rotated 0.11 revolutions.