# Momentum: How can a rolling wheeled vehicle turn 180 degrees without stopping?

"In Newtonian mechanics momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an external force."

How then, is it possible for a rolling wheeled vehicle to turn 180 degrees (reversing the direction of its momentum/kinetic energy) without stopping?

An example: when driving my car, to bring my forward kinetic energy to zero I apply my brakes and convert it to heat energy. To move in the opposite direction I then need to set the gearbox in reverse and apply extra energy. Yet if I switch off the engine (adding no new kinetic energy) and turn the wheel, then I can achieve the same effect (with small losses due to wheel friction) without dispersing or exerting any energy. How is this possible?

How can a rolling wheeled vehicle turn 180 degrees without stopping ?

The answer is in the last sentence of the passage you quote:

An object will stay still or keep moving at the same speed and in a straight line, unless it is acted upon by an external force

The external force that acts on a coasting car to change its direction is the sideways friction between the car's tyres and the road. If the road were perfectly smooth then you could not steer the car. Similarly, if the car's wheels could not turn at an angle to its direction of motion, then it could not be steered.

There are vehicles without steerable wheels, but they all use various mechanisms for creating a difference in friction from one side of the vehicle to the other. A sledge is steered by the rider shifting their weight from one side to the other. A tank is steered by making its tracks move at different speeds.

• See also my comment to the first answer. The question is how sideways friction changes the direction of the momentum of the object, rather than just adding a new directional component. Commented Nov 14, 2022 at 7:36
• @DanielBoyd The momentum vector of an object always points in the direction of travel. Any applied force that is at an angle to the direction of travel (such as sideways friction) will add a new momentum vector at an angle to the current vector. This will therefore change the direction of the object's momentum vector, and hence change its direction of travel. Commented Nov 14, 2022 at 8:18

Take note of the last part of Newton's law quoted above that states unless it is acted upon by an external force. If there are no externals forces, an object will remain at rest or in a state of uniform motion with constant velocity.

The examples you provide include the existence of external forces. Namely, the frictional forces provided by the road on the tyres.

• Certainly I appreciatie that there are external forces at work, but I would expect these to be additive: that they could cause the vehicle to move sideways in addition to its existing forward movement. What puzzles me is how the direction of the forward motion can be reversed by such forces, which are minor compared with those required to bring it to a halt and then accelerate it to the same opposite velocity. Commented Nov 12, 2022 at 16:22
• @DanielBoyd The change in momentum is the same no matter whether the vehicle stops and reverse in a straight line, does a handbrake turn, or turns gradually through 180 degrees by cornering. A small force can produce a large change in momentum if it is applied over a long enough time. Commented Nov 14, 2022 at 8:22

Think of the semicircular motion of a body which is moving at constant speed.
That body must have a force on it to cause the centripetal acceleration which in the case of a vehicle is provided by the force of friction on the tyres due to the road.

• It seems that centripetal acceleration could be the answer. While usually applied to bodies that are restricted to moving in a straight line (e.g. a pendulum on a string or a planet captured by the gravitational force of its sun) this would seem to be comparable physics. I guess then my puzzlement is how centripetal acceleration manages to change a moving object's direction without reducing it, since momentum is directional ! Commented Nov 14, 2022 at 7:43