Preview
Circular Motion & Centripetal Force
Why objects curve instead of fly off
Take a ball for a spin on a string and your body will swear an oath: something is pulling that ball outward, straining against your grip. Your hand aches from fighting it, so the outward pull must be real — right? Cut the string in your imagination and interrogate that instinct: if an outward force were doing the pulling, the ball would sail away from the center the moment it was free. It doesn't. It flies off along the tangent, in a perfectly straight line, because the instant the string lets go there is no horizontal force on the ball at all. The only force that ever acted was yours, pulling inward, through the string. The 'outward force' was never on the ball — it was the ball's own inertia pushing back on your hand as your hand dragged it off the straight path it wanted. That inversion is the whole lesson: circular motion is not a balance between inward and outward pulls, it is a one-sided inward pull constantly steering a ball that would otherwise go straight. And it is a demanding pull: double the speed and the required force does not double, it quadruples — the reason highway curves are banked and exit ramps carry speed limits. In this lab you will watch the arrows themselves deliver the verdict — velocity always tangent, acceleration always aimed at the pivot, and no arrow anywhere pointing outward — then clock the force quadrupling under your own fingertips, read the banking angle off a car taking a curve, and check whether a roller coaster clears the top of its loop.
What you'll be able to do
- Explain that circular motion is produced by a net inward force provided by ordinary forces (tension, normal, gravity) — never by a new 'centripetal force' and never balanced by an outward 'centrifugal force' — and identify the provider in the conical-pendulum, banked-curve, and vertical-circle scenarios
- Apply a_c = v²/r, F_c = mv²/r, T = 2πr/v, and ω = v/r to compute the panel's readouts — e.g. at the default state (m = 1.0 kg, v = 4.0 m/s, r = 2.0 m): a_c = 8.00 m/s², F_c = 8.00 N, T = 3.14 s, ω = 2.00 rad/s — and predict that doubling speed quadruples the required force
- Use the design-speed condition tan θ = v²/(rg) to read the banked/conical angle (50.8° at the Banked Curve preset) and v_min = √(rg) to judge the vertical circle (4.43 m/s at r = 2 m — the 5.0 m/s preset clears it)
Formulas
Make a prediction
Default setup: a 1.0 kg ball swings in a horizontal circle of radius 2.0 m at 4.0 m/s, held by the string from the pivot above. Before you open the Show Vectors view — which force picture is correct?
No grading here — commit to a guess, then scroll down and test it yourself.
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Check
Did the lab agree with you?
Your prediction
You skipped the prediction — jump back to the preview and commit to a guess first; the comparison is the whole point.
Answer: Only an inward pull acts: the string's tension has a horizontal component pulling the ball toward the center — F_c = mv²/r = 1×16/2 = 8.00 N — and no outward force exists anywhere; if the string let go, the ball would fly off along the tangent
Newton's second law leaves no room for a balance: the ball is accelerating — its velocity's direction changes every instant — so the net force cannot be zero. It must point the way the acceleration points, toward the center, with magnitude F_c = mv²/r = 1.0×(4.0)²/2.0 = 8.00 N, supplied here by the horizontal component of the string's tension (the panel's d-ac and d-fc rows read 8.00 m/s² and 8.00 N at this state). The 'centrifugal force' of option B is the single most documented false friend in this unit — OpenStax University Physics states it verbatim: 'centrifugal force... does not actually exist... centrifugal force is a fiction' (§6.3). If two balanced forces really acted, releasing the string would leave the ball at rest or drifting — instead it continues along the tangent at 4.0 m/s, because with the tension gone the net force is zero and Newton's first law takes over: straight line, constant velocity. Option C is the research-documented 'curvilinear impetus' belief (McCloskey, Caramazza & Green, Science 1980): most people predict a released object keeps curving, but nothing pushes the ball forward — it keeps its 4.0 m/s because inertia needs no help, and the green velocity arrow in the Show Vectors view is tangent at every instant precisely because the tangent is the path inertia would choose. What your hand feels when you spin a real ball is the reaction to the inward pull you supply — the ball's inertia pressing outward on you, not a force pulling outward on the ball.
Quiz (0/3)
A 2 kg ball moves at 6 m/s in a circle of radius 3 m. What centripetal force is required?
If you double the speed while keeping radius fixed, how does the centripetal force change?
A car rounds a flat curve of radius 50 m at 20 m/s. What friction force is needed? (m = 1200 kg)
You can now
- Explain that circular motion is produced by a net inward force provided by ordinary forces (tension, normal, gravity) — never by a new 'centripetal force' and never balanced by an outward 'centrifugal force' — and identify the provider in the conical-pendulum, banked-curve, and vertical-circle scenarios
- Apply a_c = v²/r, F_c = mv²/r, T = 2πr/v, and ω = v/r to compute the panel's readouts — e.g. at the default state (m = 1.0 kg, v = 4.0 m/s, r = 2.0 m): a_c = 8.00 m/s², F_c = 8.00 N, T = 3.14 s, ω = 2.00 rad/s — and predict that doubling speed quadruples the required force
- Use the design-speed condition tan θ = v²/(rg) to read the banked/conical angle (50.8° at the Banked Curve preset) and v_min = √(rg) to judge the vertical circle (4.43 m/s at r = 2 m — the 5.0 m/s preset clears it)