1.2.16 · D5Newton's Laws & Dynamics
Question bank — Centripetal force — what provides it in various situations
How to use this page
True or false — justify
Uniform circular motion has zero acceleration because the speed is constant.
False — velocity is a vector; its direction rotates even when its length is fixed, so and points to the center (Figure s01).
Centripetal force is a distinct fundamental force alongside gravity and electromagnetism.
False — it is only a name for whatever real force supplies the inward pull; the four fundamental forces are unchanged.
If you draw a free-body diagram, you should add an arrow labelled "centripetal force."
False — you draw only real forces (tension, gravity, normal, friction); then you set their net inward component equal to . Adding a separate arrow double-counts.
Doubling the speed of a car on the same curve requires twice the inward force.
False — scales with , so double speed needs four times the inward force.
For a satellite in a circular orbit, gravity does work on it and speeds it up.
False — gravity points to the center, perpendicular to the velocity, so it does zero work; the orbital speed stays constant.
On a frictionless banked road there is exactly one speed for which no friction is needed.
True — (with from the horizontal) fixes a single for a given angle; above it you slide up, below it you slide down, so friction is needed off that speed.
A charge moving through a magnetic field is sped up by the magnetic force as it circles.
False — the magnetic force is always perpendicular to , so it does no work; it changes direction only, keeping speed constant.
At the top of a vertical loop the string tension points upward.
False — at the top the string runs toward the center, which is below the bob, so tension points downward, adding to gravity: (Figure s02, right).
The centrifugal force is what actually throws you against the car door in a sharp turn.
False — in the ground (inertial) frame there is no outward force; your body's inertia keeps it going straight while the door curves into you. Centrifugal force only exists as a pseudo-force in the rotating frame.
Increasing the radius of a curve always makes it safer at a given speed.
True — required falls as grows, so a wider curve needs less friction/banking for the same speed, leaving more margin before skidding.
Spot the error
A student writes, for a car on a flat curve: " always, so at every speed."
Error: equals only at the skid limit. Below that, friction supplies exactly , which is less than the maximum; is the maximum speed, not the actual one.
A student writes for the conical pendulum: " is the centripetal force." (Here is the string's angle from the vertical, as in Figure s03.)
Error: with measured from the vertical, the horizontal component is — that points inward and is the centripetal force; the vertical component balances gravity ().
A student writes at the top of a loop: "."
Error: sign flip. Both and point inward (down), and together they equal the required inward force: , so .
A student sets up orbit as " so " for a satellite far from Earth.
Error: gravity out there is , not ( is only the surface value). Correct: .
A student says: "On a banked road, friction is never involved, so holds at all speeds."
Error: (with from the horizontal) is the frictionless design equation for one specific speed. At other speeds friction contributes, and the real safe range is a band around that ideal speed.
A student writes for a charge in a field: ", so faster charges circle in smaller loops."
Error: is proportional to (it's in the numerator), so faster charges circle in larger loops, not smaller.
A student, for a banked road, writes " is the centripetal force" using measured from the horizontal.
Error: with from the horizontal, the horizontal (inward) component of is ; that is the centripetal force, while is vertical and balances (Figure s03, left).
Why questions
Why does the ball fly off in a straight line the instant you release the string, rather than spiralling out?
Because once tension vanishes there is no inward force; by Newton's first law the ball keeps its current velocity, which is tangent to the circle — a straight line.
Why is the required force called "centripetal" (center-seeking) and never "centrifugal"?
Because the net real force that bends the path must point toward the center to curve the motion inward; an outward net force would push the object away from the circle.
Why can't static friction supply unlimited centripetal force on a flat curve?
Static friction is capped at ; once the demand exceeds this ceiling, friction saturates, the wheel breaks grip, and the car skids outward.
Why does banking a road let a car turn faster without relying on friction?
Tilting the road tilts the normal force so it gains an inward horizontal component (with from the horizontal), which does the centripetal job on its own, so grip isn't needed to make the turn.
Why does a minimum speed exist at the top of a vertical loop but not at the bottom?
At the top gravity already points inward; if is too small the needed is less than , so the string can't push (it goes slack) and the object falls. At the bottom gravity points outward, so tension can always be increased to supply any .
Why does a magnetic force curve a charge's path but never change its speed?
Because is always perpendicular to , so : zero work, hence constant kinetic energy and constant speed, only turning.
Why does the derivation use the velocity triangle rather than the position triangle?
Because acceleration is the rate of change of velocity; we need , so we build the isosceles triangle from the two velocity vectors (each length ) turning through (Figure s01).
Edge cases
What is the centripetal acceleration when (object momentarily at rest, e.g. a pendulum at its highest swing point)?
With the object is not instantaneously moving in a circle at all, so strictly (a circular-path radius) isn't defined by the motion; taking the limit, the inward acceleration required for circular motion is — no centripetal force is needed at that instant because the path isn't curving yet.
What happens to the minimum top-of-loop speed as the radius shrinks toward zero?
: a tiny loop needs almost no speed at the top, because the required can match even for small .
For a car on a flat road, what is the maximum turning speed if the road is perfectly frictionless ()?
— with no friction and no banking there is nothing to supply , so the car cannot turn at all; it goes straight.
In the banking formula , what banking angle is needed for a straight road ()?
, so (measured from the horizontal): a straight road needs no banking, consistent with no inward force being required.
If a satellite's orbital radius , what happens to its required orbital speed?
: far-out orbits are slower, because the weakening gravity supplies less centripetal force and demands a smaller .
What net inward force acts on a body moving in a straight line at constant velocity?
Zero — a straight path has infinite radius, so ; no centripetal force is needed, matching Newton's first law.
Recall One-line summary of every trap
Centripetal force is a requirement (, with ) met by real forces; it always points inward, does no work when perpendicular to motion, is capped when supplied by friction, flips which forces help at the top vs bottom of a loop, and vanishes in every degenerate limit (, , ).