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Rotational motion of belt drive

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm just working through a few past mechanics papers and this question came up:

    A belt drives the circumference of a cylindrical wheel of radius R and mass M with
    no slipping. The tension in the belt is T. Friction in the wheel bearing causes an
    effective torque N to act on the wheel.
    (i) If the velocity of the belt is constant, what is T in terms of N.
    (ii) The bearing is lubricated removing all significant friction and the velocity of
    the belt then increases with a uniform acceleration a. Write down T in terms of
    M, R, and a.

    I'd be greatful if someone could just check through my solutions so that i'm sure doing things correctly.

    2. Relevant equations

    I=0.5mR^2 for disc
    v=wr
    L=I(dw/dt)

    3. The attempt at a solution

    (i) T=N .

    (ii) v=wR implies dw/dt = a/R .

    Therefore TR = 0.5MR^2 * (a/R) ,

    and so T = 0.5Ma .

    Thanks.
     
  2. jcsd
  3. Mar 18, 2009 #2

    djeitnstine

    User Avatar
    Gold Member

    One thing I immediately noticed. In [tex]T \neq N[/tex] Why? because this is saying that Force is equal to torque. Surely you know the relationship between torque and force.
     
  4. Mar 18, 2009 #3


    Ah yeah woops! Should be T=N/R ?

    Thanks.
     
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