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How can we solve this and what’s the answer

How can we solve this and what’s the answer-example-1
User DMabulage
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1 Answer

6 votes

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.

User VBart
by
8.1k points

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