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Math Help - Angular deceleration of wheels.

  1. #1
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    Angular deceleration of wheels.

    Right, so I have been stuck on this question for a while now but not sure where to start. I'm almost pulling my hair out, any guidance or pointers would be appreciated.

    I need to calculate the angular deceleration of wheels of a lorry. It needs to stop in 0.5km using constant braking force.

    It's weight is 5 tonnes and velocity is 80 km h-1. The wheels are 1.5m in diameter.

    So far I've worked out the deceleration of the lorry (-0.494 ms-2), the braking force required (-2.4kN), the time taken to come to rest (2024.29), and the initial angular velocity of the wheels (29.63 rad/s).

    Just can't get my head around the "angular deceleration" part. Can someone please tell me where to start.

    Regards,

    Becca.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    You can use the same formula as with linear speed acceleration/deceleration.

    v^2 = u^2 + 2as

    v = 0,
    u = initial angular velocity
    a = acceleration or deceleration
    s = angular displacement
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  3. #3
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    Hi, thanks for the reply.

    Could I use alpha=dw/dt?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Unknown008 View Post
    You can use the same formula as with linear speed acceleration/deceleration.

    v^2 = u^2 + 2as

    v = 0,
    u = initial angular velocity
    a = acceleration or deceleration
    s = angular displacement
    Quote Originally Posted by becca View Post
    Hi, thanks for the reply.

    Could I use alpha=dw/dt?
    You do not have d \omega/dt in order to do this. However you have the initial angular speed (you know the radius of the wheel and the linear speed, so v_0 = r \omega _0 ). You know the final angular speed, and you know the angular distance the wheel has gone through. ( s = r \theta ) So you can use the angular analogue of Unknonw008's equation: \omega ^2 = \omega _0^2 + 2 \alpha \theta .

    By the way, the two equations v_0 = r \omega _0 and s = r \theta are known as the "rolling without slipping" conditions. There is one more: a = r \alpha . Whenever a wheel is moving without slipping these relations relate the linear variables (s, v, and a) to the rotating variables ( \theta, \omega, and \alpha.)

    -Dan
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  5. #5
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    Hi Dan,

    Thanks for the reply.

    So using your formula for acceleration I get:

    α=(ω_0^2- ω^2)/θ

    α=(29.63-0)/6.28

    α = -69.90 rad/s^2

    p.s. what software/program do you use to display your formulas like you do?

    Thanks,

    Becca.
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