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3 October, 01:14

A solid cylinder with a radius of 73.3 cm and a mass of 2.33 kg accelerates

uniformly from rest in 4.13 seconds while experiencing 6.71 rotations.

Solve for the (a) final angular velocity.

- Solve for the (b) the torque required to produce the angular acceleration.

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Answers (1)
  1. 3 October, 02:12
    0
    (a) 20.4 rad/s

    (b) 3.09 Nm

    Explanation:

    Given:

    Δθ = 6.71 rev = 42.2 rad

    ω₀ = 0 rad/s

    t = 4.13 s

    Find: ω

    Δθ = ½ (ω + ω₀) t

    42.2 rad = ½ (ω + 0 rad/s) (4.13 s)

    ω = 20.4 rad/s

    Find: α

    Δθ = ω₀ t + ½ αt²

    42.2 rad = (0 rad/s) (4.13 s) + ½ α (4.13 s) ²

    α = 4.94 rad/s²

    ∑τ = Iα

    τ = ½ m r² α

    τ = ½ (2.33 kg) (0.733 m) ² (4.94 rad/s²)

    τ = 3.09 Nm
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