Circular Motion and Gravitation
Identify inward force and tangential motion, calculate circular quantities, and reason about gravity, weight, satellites, and orbital changes.
Circular Motion and Gravitation
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Velocity is tangent; acceleration and net force are inward
An object moving in a circle continually changes velocity direction even when its speed is constant. The required acceleration points toward the center.
ac = v²rFc = mv²r“Centripetal force” is not an extra kind of force. It is the name for the net inward force, which may be supplied by tension, friction, gravity, a normal force, or a combination.
Fgravity = Gm₁m₂r²weight = mgVelocity is tangent
If the inward force disappears, the object initially follows the tangent.
Force is inward
Centrifugal force is not an additional outward force in an inertial-frame force diagram.
Speed has a squared effect
At fixed m and r, doubling v requires four times Fc.
Gravity follows an inverse square
Doubling center-to-center separation reduces force to one-fourth.
Orbit is continuous free fall
Tangential speed carries the satellite forward while gravity curves its path.
At any point, draw TANGENT and INWARD
TANGENT: Direction of instantaneous velocity.
INWARD: Direction of centripetal acceleration and net force.
Then identify which real force supplies the inward result. For comparisons, use proportional reasoning before substituting numbers.
Why it works
Most circular-motion mistakes come from pointing velocity inward, inventing an outward force, or ignoring the squared speed and inverse-square distance relationships.
Five forms you should recognize
Problem: A 2 kg object moves at 4 ms in a radius of 2 m.
Fc = 2(4²)÷2 = 16 N inwardIts velocity remains tangent to the circle.
Problem: A stone travels in a circle and its string breaks.
Conclusion: Tension disappears, so the stone initially follows the tangent at the release point—not a radial line outward.
Problem: Center-to-center distance doubles.
Fnew = Fold÷2² = Fold÷4Problem: A 60 kg person stands where g = 1.6 ms².
weight = 60(1.6) = 96 NMass remains 60 kg.
Problem: Why does a satellite not fall straight down?
It is falling under gravity, but its tangential speed carries it forward so the surface curves away as its path curves inward.
Check before you commit
- Pointing circular velocity toward the center
- Adding a separate centripetal force to the real inward forces
- Assuming constant speed means zero acceleration
- Measuring gravitational separation surface-to-surface
- Changing mass when only location changes
- Claiming gravity is absent in orbit
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Circular Motion and Gravitation FAQ
What supplies centripetal force?
It depends on the situation: tension, friction, gravity, a normal force, or a combination can provide the net inward force.
Why do astronauts feel weightless if gravity acts?
They and their spacecraft share free fall, so the supporting normal force is nearly absent.
Do heavier satellites orbit faster?
Not at the same circular-orbit radius around the same central body; satellite mass cancels from the orbital-speed relation.
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