Grade 12 · Week 08 · Monday · Day 01

A Turn at Constant Speed

Guiding question: Why does turning require acceleration even when speed remains unchanged?

Objective: Explain velocity direction, centripetal acceleration and inward net force using vector reasoning.

45–60 minutes · No apparatus · Standalone offline lesson

Learn the science

Speed is not the whole velocity

Velocity is a vector with magnitude and direction. A bicycle rounding a curve at a steady 4 m/s keeps its speed constant but continually changes the direction of its velocity. Acceleration is change in velocity per unit time, not merely change in speed. A circular path therefore requires a net acceleration toward the center even when the speedometer reading stays steady.

Name the inward direction

For uniform circular motion, centripetal acceleration has magnitude a_c=v²/r, where v is tangential speed in m/s and r is circle radius in meters. Its direction points toward the center at each instant. The net radial force is F_net,radial=m v²/r. Centripetal describes the direction of the RESULTANT force; it is not an extra force you add alongside real interactions such as friction, tension or gravity.

What the moving arrow represents

Velocity is tangent to the circular path at each position while acceleration points toward the center. The velocity arrow changes its direction continuously. If all radial forces suddenly disappeared, the body would continue approximately along the instantaneous tangent under Newton's first law, rather than flying outward under an invented force.

Check the model’s boundaries

The digital investigation assumes an ideal particle traveling at constant speed around a circle. It does not model the mechanism maintaining that path. Real vehicles can turn using tire-road contact friction; a tethered object can turn under tension; planets orbit under gravity. Actual situations can also have a tangential acceleration if speed changes.

Vocabulary

speed
Nonnegative magnitude of velocity, in m/s.
velocity
Vector describing motion rate and direction.
centripetal acceleration
Inward acceleration for circular motion with magnitude v²/r.
tangent
Straight direction of the instantaneous velocity of circular motion.
radial net force
Sum of real forces' inward components, equal to mv²/r for uniform circular motion.

Worked example

A 2 kg object moving at 4 m/s around a circle of radius 8 m has a_c=4²/8=2 m/s² inward. The required net inward force is F_c=2×2=4 N. Its velocity is tangent to the circle, not inward.

Calculate independently and write the units and directions.

Independent evidence journal

Draw velocity and net-force arrows at the top, right and bottom of a circular path, then use the Circular Motion Studio to compare identical speeds with different radii.

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Daily Practice · 4 Questions

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