계산 방법 구심력 (F = mv²/r): 공식 & 예제
계산 centripetal 힘 with F = mv²/r, convert km/h safely, and rearrange for 속력 or radius. Verify every answer with a free centripetal 힘 calculator.
What 구심력 Means
Centripetal 힘 is the net inward 힘 that keeps an object moving in a circle. Even when 속력 is constant, direction keeps changing, so there is a continuous inward 가속도 a = v²/r. Newton’s second law then gives F = m a = m v² / r.
The word “centripetal” describes the required direction — toward the centre. Tension in a string, friction on a flat turn, gravity in orbit, or a normal 힘 on a banked curve can supply that inward net 힘. The 공식 tells you how large it must be.
If you already have 질량, 속력, and radius and only need a 확인ed number, open the free centripetal 힘 calculator first, then return here for unit traps and 일ed examples.
The 공식 F = mv²/r
For uniform circular motion:
If the problem gives angular 속력 ω in rad/s, use F = m ω² r (and remember v = ω r). Stay with mv²/r when linear 속력 is given.
단위 That Keep Marks Safe
Trap: 72 km/h is 20 m/s. Leaving 72 in F = mv²/r inflates 힘 by more than an order of magnitude because 속력 is squared.
풀이 예제
예제 1: 2.0 kg at 4.0 m/s, r = 2.0 m
F = (2.0)(4.0)² / 2.0 = 32 / 2.0 = 16 N toward the centre. 확인 with a = v²/r = 16/2 = 8 m/s², then F = ma = 16 N.
예제 2: find 속력 from 45 N
A 5.0 kg 질량 needs 45 N on a 5.0 m radius. v = √(45 × 5.0 / 5.0) = √45 ≈ 6.71 m/s. 확인: m v² / r ≈ 45 N.
예제 3: km/h conversion
A 0.50 kg ball on a 1.0 m string moves at 36 km/h. First v = 36 / 3.6 = 10 m/s. F = (0.50)(10)² / 1.0 = 50 N. Using 36 without converting wrongly suggests hundreds of newtons.
Centripetal vs Centrifugal
In the usual school (inertial) frame, draw real 힘s and require their net radial component to equal mv²/r inward. “Centrifugal 힘” is a fictitious outward 힘 used in rotating frames. Do not add both in the same free-body diagram.
For straight-line F = ma problems without a circle, use the 힘 calculator.
흔한 실수
Sanity 확인: for a few kilograms at everyday walking 속력s on a metre-scale radius, F is often tens of newtons — not kilonewtons.
확인 With the 무료 계산기
The centripetal 힘 calculator applies F = mv²/r with visible steps so you can verify 힘, 속력, or radius.
Centripetal 힘 calculator — F, v, or r.
힘 calculator — F = ma.
속도 calculator — find 속력 for circular problems.
마찰 calculator — when friction supplies the turn.
학습 F = mv²/r with clean SI 단위, then confirm every answer on the calculator.