Banked Turn with Friction - Physics of Speed Limits on Banked Curves

We take a look at the general case of finding the maximum speed at which a car can drive around a banked curve without skidding out. You can skip right to the result at 7:48 if you'd like. 0:00 We set up the problem using F = ma (Newton's 2nd Law) in the vertical (a = 0) and horizontal (a = mv^2 / R) directions to 4:17 relate the maximum speed to the ramp angle, radius of curvature of the road, and the coefficient of friction. Finding the speed limit on a banked curve is a very standard problem in mechanics in undergraduate physics, AP Physics, and IB Physics, and is useful for those who design banked roads. 7:48 Finally, we show the specific results for maximum speed vs. ramp angle for the specific case of an exit ramp radius of curvature of 100 m, acceleration due to gravity of 10 m/s^2, and a coefficient of friction of 0.9, which is reasonable for a dry day for rubber on asphalt. In addition, we explore what would happen if the road were unbanked and if the road were banked (tilted) the wrong way.