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23 July, 09:09

Your roommate is working on his bicycle and has the bike upside down. He spins the 60 cm

diameter wheel, and a pebble in the tread goes by 3 times every second.

what is the pebbles speed and acceleration?

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Answers (1)
  1. 23 July, 09:19
    0
    Diameter = 60 cm, Radius = 60/2 = 30 cm = 30/100 = 0.3 m.

    The pebble in the tread goes by 3 times every second.

    This is the same as 3 times per second.

    Recall the unit of frequency is Hertz or per second, s⁻¹

    So 3 times per second, Frequency, f = 3s⁻¹ or 3 Hertz

    For angular motion:

    Angular speed, ω = 2πf

    = 2*π*3

    = 6π rad/s

    Linear speed, v = ωr = 6π * 0.3 = 1.8π m/s

    Linear acceleration, a = v² / r

    a = 1.8π * 1.8π / 0.3 = 10.8π² m/s²

    Angular acceleration α = a/r = 10.8π² / 0.3 = 36π² rad/s²

    Angular speed = 6π rad/s ≈ 18.840 rad/s

    The linear speed of the pebble = 1.8π m/s ≈ 5.655 m/s

    The angular acceleration = 36π² rad/s² ≈ 355.306 rad/s²

    The linear acceleration of the pebble = 10.8π² m/s ≈ 106.592 m/s²
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