Why are heavy shopping carts much harder to turn than they are to push forward?
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Because it’s a lever.
Pushing your cart forward transfers 100% of the force in direction of movement, over 100% of the way you pushed.
Turning it means you move the tip of the cart around you while (more or less) standing in place and moving the handle very little. For the two sides of a lever, the product of force and length is equal, so when you move the closer end just a little and the far end moves a lot, only a fraction of the force you applied gets transferred. That means in order to accelerate the tip of the cart by an amount you deem appropriate you need a way stronger force compared to just pushing the cart forward.
This works the other way as well: if you keep the tip of your cart in place and turn it by moving the handle around that turning point, you will find it easier to move the cart at all, for the tradeoff of having to apply the force over a longer distance, i.e. you have to walk along the circle with your carts handles.
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