Rolling race
A sphere, a cylinder and a hoop roll down a slope together. Which reaches the bottom first?
When an object rolls without slipping down an incline, its gravitational potential energy turns into both translational and rotational kinetic energy. The larger the moment-of-inertia factor k = I/(mR²), the more energy goes into rotation and the slower the object moves down the slope. The solid sphere has the smallest factor, k = 2/5, and always arrives first; the hoop, with k = 1, is the slowest. The result depends on neither the mass nor the radius of the objects.
Speed vs. time for the three objects
The slope of each line is the acceleration: steepest for the solid sphere, gentlest for the hoop. Speeds stay constant after reaching the bottom.
Think about it
If the hoop is replaced by a heavier, larger hoop, can it beat the solid sphere?
No. The acceleration a = g·sinθ/(1 + k) depends only on the shape factor k, not on mass or radius. As long as the shape stays the same, a hoop is always slower than a solid sphere.
Model assumptionsRolling without slipping · Rolling friction and air resistance neglected · Released together from rest
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.