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Homework Help: Finding the Velocity and Acceleration of a Car in Circular Motion

  1. Sep 13, 2013 #1
    1. The problem statement, all variables and given/known data
    A car enters the circular road with radius r = 200m at a
    speed of v = 80km/h. A radar gun at O needs to rotate with constant angular
    acceleration d^2θ/dt^2 = 0.025 rad/s2 to follow the motion of the car along the circular road.
    a) Determine the acceleration of the car at the instant right after it enters the circular
    b) Determine the velocity and acceleration of the car at the instant when the radar
    gun has rotated

    2. Relevant equations

    v_r = dr/dt
    v_θ = r(dθ/dt)
    a_r = dr/dt - r(dθ/dt)^2
    a_θ = r(d^2θ/dt^2) + 2(dr/dt)θ

    3. The attempt at a solution

    I think I got a right.

    I took derivatives of the radius which is zero, and integrated the angular acceleration. I then just plugged the numbers into the acceleration formulas and got a_r=0 (assuming t=0) and a_θ = 5 = a.

    I am a bit unsure about the 2nd one because i am having trouble getting the equation of velocity and acceleration in terms of theta. I always end up with either the angular velocity, or time variable in there. Help appreciated.
  2. jcsd
  3. Sep 13, 2013 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    I am not sure what the question is in part b). Is it the speed of the car when it has rotated 2π radians?

    r is constant, since it is a circle. So you don't need to worry about dr/dt

    You first have to find how long it takes the car to make the full circle: Δt. Then find the Δv in that time.

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