Gravity makes a huge difference in calculating weight; however, the mass doesn't change.
As for turning corners and stopping etc: Momentum is m*v. the m did not change so momentum still rules.
Explain the following quote:
... it was several weeks before an emigrant from Earth could adapt to it. On the Moon
the human body had to learn a whole set of reflexes. It had, for the first time, to
distinguish between mass and weight.
A man who weighed one hundred eighty pounds on earth might be delighted to
discover that he weighed only thirty pounds on the Moon. As long as he moved in a
straight line at a uniform speed he felt a wonderful sense of buoyancy. But as soon as
he attempted to change course, to turn corners or to stop suddenly
–
then
he would find
that his full one hundred eight pounds of mass, or inertia, was still there. For that was
fixed and unalterable
–
the same on Earth, Moon, Sun, or in free space. Before one
could be properly adapted to lunar living, therefore, it was essential to learn that all
objects were now six times as sluggish as their mere weight would suggest. It was a
lesson usually driven home by numerous collisions and hard knocks, and old lunar
hands kept their distance from newcomers until they were acclimatized.
-- Arthur C. Clarke. (2001: A Space Odyssey)
My answer- This quote is telling us that force of gravity makes a huge difference when calculating mass and weight.
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