Revise: Forces in Circular Motion
What actually supplies the centripetal force in circular motion β tension, friction, gravity, or a banked track β vertical circles, and why centrifugal force is a fictitious force.
Fc = mvΒ²/r β always points toward the centre of the circle.
m=0.5kg, v=4m/s, r=0.8m β Fc=10N.
For a ball on a string, tension alone supplies the centripetal force.
m=0.2kg, r=0.5m, Ο=5rad/s β T=2.5N.
Maximum safe turning speed: v_max = β(ΞΌgr).
ΞΌ=0.4, g=9.8, r=50m β v_max=14 m/s.
Bottom of loop: T = mvΒ²/r + mg. Top of loop: T = mvΒ²/r β mg.
m=2kg, v=5m/s, r=1m at bottom β T=69.6N.
Centrifugal force isn't real β it's your inertia resisting the turn, felt from inside a rotating frame.
A car door pushes YOU inward; you only feel pushed outward against it.
The net inward force needed for any circular motion; not an extra force of its own.
m=2kg, v=10m/s, r=5m β Fc=40N.
A string can only pull along its length β automatically toward the centre for horizontal circular motion.
m=0.3kg, r=0.4m, Ο=4rad/s β T=1.92N.
Friction has a maximum value (ΞΌmg) β exceeding it means the car skids outward off the curve.
ΞΌ=0.5, g=9.8, r=20m β v_maxβ9.9 m/s.
For orbiting objects, gravity alone supplies Fc β astronauts are in continuous free fall, not beyond gravity.
m=500kg, v=8000m/s, r=8Γ10βΆm β Fc=4000N.
Gravity helps supply Fc at the top of a vertical loop, opposes it at the bottom.
m=1.5kg, v=4m/s, r=0.8m at bottom β T=44.7N.
Only the inward centripetal force is real; the outward feeling is inertia, not a force.
Cutting a swung string removes Fc; the ball flies off straight, not outward.
Banking angles the normal force inward, letting it help supply Fc β even with zero friction.
v=25m/s, r=100m β ideal banking angle β32.5Β°.
Same physics (Fc = mvΒ²/r) in centrifuges, washing machines, roller coasters, and orbits β only the force source changes.
A centrifuge wall pushes denser particles inward, separating them by density.