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The Car Differential Worksheet
By the end you will: explain why the wheels of a turning car travel different distances, and how a differential lets them turn at different speeds.
A. Explore with the simulation
Set the speed to 36 km/h. Steer to full lock, then half lock, and fill in the table.
Steering Turn radius (m) Inner wheel (km/h) Outer wheel (km/h) Outer ÷ inner Full lock Half lock Compare the carrier's rpm with the two wheels' rpm while turning. What rule links them?
Turn on “Lock the axle” and turn. What happens to the tyres?
Turn off the lock and put the right rear wheel on ice. What happens?
B. Calculate
A car turns on a circle of radius 10 m (to the middle of the axle). Its wheels are 1.5 m apart. Find the radius each rear wheel follows, and the ratio of their speeds.
The left wheel turns at 400 rpm and the carrier at 350 rpm. How fast is the right wheel turning?
C. Think it through
Why do off-road vehicles have a button to lock the differential?
Answer key (for teachers and parents)
- Full lock: 3.5 m, inner 28.3 km/h, outer 43.7 km/h, 1.55× · Half lock: 7 m, 32.1 km/h, 39.9 km/h, 1.24×. Sharper turns make a bigger difference.
- The carrier always turns at the average of the two wheels: (left + right) ÷ 2.
- Both wheels must turn at the same speed, so the tyres scrub and skid sideways round the corner.
- The ice wheel spins at twice the carrier speed and the car doesn't move: an open differential sends the drive to the wheel that's easiest to turn.
- Inner 10 − 0.75 = 9.25 m, outer 10 + 0.75 = 10.75 m. Ratio = 10.75 ÷ 9.25 ≈ 1.16.
- (400 + right) ÷ 2 = 350, so right = 300 rpm.
- On mud or ice one wheel can spin uselessly. Locking makes both wheels turn together, so the one with grip can push the car out.
Free to print and share for teaching. Made with the interactive simulation at jugnix.com/simulations/differential.