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
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
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.