converting linear velocity to angular velocity

MURTUZA ZAVERI

MURTUZA ZAVERI

@murtuza-cekSdZ • Oct 26, 2024
THE title of this thread might appear to be quite misleading or something, but i did not know how best to put it though.

now here is a situation:

a dead weight weighing 10 kg has been hoisted up to a certain height, by a rope and pulley mechanism. it is then made to remain hanging there, by tying the other end of the rope to some support.

now if all of a sudden, if the other end of the rope was released, causing the weight to fall freely, and dragging the rope with it, through the pulley, then what would be the rpm of the rotating pulley ?

by using the formulas of potential and kinetic energies, the velocity of the falling weight can be determined. now how do i use this to find the rotational speed of the pulley
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  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • Jul 18, 2017

    Assuming that the rope is inelastic, there is no slip between the rope and the pulley, and the pulley is frictionless, the speed of the weight is given by:
    V=0.5 g t^2.
    RPM = V/(pi X d) d is the pulley diameter
    This means that the pulley RPM continuously increases.
    Atwood's Machine demonstrates this.
    #-Link-Snipped-#
    We had this in our high school.
    Personally this experiment was the one that made me decide on a research career in 1953.
    0
  • MURTUZA ZAVERI

    MURTUZA ZAVERI

    @murtuza-cekSdZ • Jul 18, 2017

    thankyou Ramani sir
    0
  • MURTUZA ZAVERI

    MURTUZA ZAVERI

    @murtuza-cekSdZ • Jul 18, 2017

    A.V.Ramani
    Assuming that the rope is inelastic, there is no slip between the rope and the pulley, and the pulley is frictionless, the speed of the weight is given by:
    V=0.5 g t^2.
    RPM = V/(pi X d) d is the pulley diameter
    This means that the pulley RPM continuously increases.
    Atwood's Machine demonstrates this.
    #-Link-Snipped-#
    We had this in our high school.
    Personally this experiment was the one that made me decide on a research career in 1953.
    sir,

    what about the units of the formulas you just provided.
    0
  • Ramani Aswath

    Ramani Aswath

    @ramani-VR4O43 • Jul 19, 2017

    V - velocity m/sec
    t - time from start in seconds
    g - acceleration due to gravity = 9.8 m/sec^2
    d - diameter in m
    Pi - 3.1416
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  • MURTUZA ZAVERI

    MURTUZA ZAVERI

    @murtuza-cekSdZ • Jul 19, 2017

    thanx again sir
    0