Banked Turn

v = [g r {sin(q)+m cos(q)} / {cos(q) - m sin(q)} ]1/2

Notice that the mass cancels out. This means that the mass of the car does not matter! (Big heavy trucks slip on slippery streets just like small cars. When going fast, big heavy trucks flip over rather than slide off the road; little cars don’t flip over like big trucks. But flipping over is not the same as slipping! We’ll look at flipping in Part 4 of the course.)

Note also that when q = 0, the above expression reduces to the one we had for a flat road:

vmax = [mgr]1/2 .

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