The car travels along the circular curve having a radius r = 400 ft. At the instant shown, its angular rate of rotation is θ = 0.025 rad/s^2, which is decreasing at the rate ¨θ = -0.008 rad/s^2. Determine the radial and transverse components of the car’s velocity and acceleration at this instant

Question

The car travels along the circular curve having a radius r = 400 ft. At the instant shown, its angular rate of rotation is \dot{ heta } = 0.025 rad/{ s }^{ 2 }, which is decreasing at the rate \ddot{ heta } = -0.008 rad/{ s }^{ 2 }. Determine the radial and transverse components of the car’s velocity and acceleration at this instant and sketch these components on the curve.

Accepted Answer

[latex]r = 400 \quad\quad \dot{ r } = 0 \quad\quad \ddot{ r } = 0 \ \dot{ heta } = 0.025 \quad\quad heta = -0.008 \ v_r = \dot{ r } = 0 \ v_ heta = r \dot{ heta } = 400(0.025) = 10 ft/s \ a_r = \ddot{ r } - r \dot{ heta }^{ 2 } = 0 - 400(0.025)^2 = - 0.25 ft/s^2 \ a_ heta = r \ddot{ heta } + 2 \dot{ r } \dot{ heta } = 400(- 0.008) + 0 = -3.20 ft/{ s }^{ 2 }[/latex]

Question : The car travels along the circular curve having a radius r =...

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