Which direction does a pendulum swing in a car going through a ramp?

Suppose you have a car going clockwise around a ramp at constant speed. A pendulum is hanging from the rear view mirror.

Does the pendulum swing outward or inward to the turn?

-

2 Answers

If the ramp is not banked, the pendulum appears in the driver's frame to swing outward. It's basically the same effect you'd get if you had a bowling ball in the back of a pickup truck. The bowling ball obeys Newton's first law and goes straight while the car turns to the right, so to someone in the car, the ball appears to go left.

If the ramp is banked, then it depends on the angle of banking and the speed of the car. If the banking angle is exactly right, so that no static friction is required between the road and the tires, then the pendulum stays sraight down in the driver's (tilted) frame. If the bank is too high in relation to the velocity, then the bob swings to the right (just as it would if the car were simply parked on a slope).

-

You ever feel yourself pulling towards the opposite direction of your turning (especially when you're getting on or off of an expressway)? It's the same situation. It's intertia at work. An object will want to keep going in the direction that it was going in. So even though you're turning, the objects within your car still have a velocity going "out" of the car.

-