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13 February, 06:20

A 2.8 kg grinding wheel is in the form of a solid cylinder of radius 0.1 m. a) What constant torque will bring it from rest to an angular velocity of 120 rad/s in 2.5 s. b) Through what angle has it turned during that time? c) What is the work done by the torque?

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  1. 13 February, 06:28
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    a) τ = 0.672 N m, b) θ = 150 rad, c) W = 100.8 J

    Explanation:

    a) for this part let's start by finding angular acceleration, when the angular velocity stops it is zero (w = 0)

    w = w₀ + α t

    α = - w₀ / t

    α = 120 / 2.5

    α = 48 rad / s²

    The moment of inertia of a cylinder is

    I = ½ M R²

    Let's calculate the torque

    τ = I α

    τ = ½ M R² α

    τ = ½ 2.8 0.1² 48

    τ = 0.672 N m

    b) we look for the angle by kinematics

    θ = w₀ t + ½ α t2

    θ = ½ α t²

    θ = ½ 48 2.5²

    θ = 150 rad

    c) work in angular movement

    W = τ θ

    W = 0.672 150

    W = 100.8 J
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