Eleventh Grade · Science · week 20

Uniform Circular Motion

Compute centripetal acceleration and centripetal force for an object moving in a circle at constant speed, and identify the real force supplying it.

An object moving in a circle at constant SPEED is still accelerating, because its velocity is a vector, and the direction keeps changing even though the magnitude does not. This acceleration points directly toward the center of the circle at every instant (which is why it is called centripetal, meaning "center-seeking"), and its size is a_c = v^2/r, where r is the radius of the circular path. By Newton's second law, this acceleration requires a net force pointing the same way: F_c = m*v^2/r, called centripetal force.

Centripetal force is NOT a new, separate kind of force to add to a free-body diagram -- it is a role that some already-familiar real force plays in a given situation. A string's tension can supply it (a ball whirled overhead); friction between tires and road can supply it (a car rounding a curve); gravity can supply it (a satellite in orbit, coming up next). The question to always ask is: "which real force here is actually pointing toward the center?"

📋 For the teacher
Teach it (10–15 min):
  • This week's lab: tie a small weight (keys, a ball in a sock) to a string and swing it in a horizontal circle overhead, well clear of people and objects. Feel how the string tension increases noticeably with a faster spin or a shorter string, exactly matching F_c=mv^2/r.
  • Drill the habit of naming the REAL force behind "centripetal force" every single time -- string tension, road friction, gravity -- rather than writing "centripetal force" on a diagram as if it were its own separate arrow.
  • Use a car rounding a curve on ice versus dry pavement as a vivid, relatable example of why a reduced available force (low friction) means a car cannot round the same curve at the same speed without sliding.
  • Explain the "flung outward" feeling on a spinning ride or in a turning car as inertia (wanting to keep going in a straight line) rather than any real outward force -- what you actually feel is the seat or door pushing you inward, toward the center, which is the real centripetal force acting on you.
Talk about it:
  • Why does an object moving at constant speed in a circle still have a nonzero acceleration?
  • What real forces can supply a centripetal force in different situations?
  • Why does a smaller-radius turn at the same speed require more centripetal force?

Mastery looks like: They compute centripetal acceleration and force for a circular-motion scenario, and correctly identify the real force actually providing it.

Common stumbles: Treating "centripetal force" as an additional force to draw on a free-body diagram rather than identifying which existing force is playing that role; believing constant speed means zero acceleration.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Science for this learner.
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