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Rolling Motion & Moment of Inertia Worksheet
By the end you will: explain why shapes roll down a ramp at different speeds, and use moment of inertia and energy to find the speed at the bottom.
A. Explore with the simulation
Set the ramp to 30° and add the ice block. Race them all and fill in the table.
Racer I Time down (s) Share of energy spinning Ice block slides Solid ball ⅖mr² Disc ½mr² Hollow ball ⅔mr² Ring mr² Change the size of every racer from 2 cm to 30 cm. Does the order or the time change? Why?
At 30°, record the speed at the bottom for the solid ball and the ring. Which is faster, and why?
B. Calculate (then check in the simulation)
Show that for a body rolling down a height h, v = √(2gh ÷ (1 + k)), where I = kmr².
A disc rolls down a ramp 2 m high. Find its speed at the bottom (g = 9.8 m/s²).
Find the acceleration of a solid ball rolling down a 30° slope.
C. Think it through
Why must there be friction for a ball to roll, and why does that friction do no work?
Answer key (for teachers and parents)
- Ice block 1.28 s · Solid ball 1.51 s · Disc 1.56 s · Hollow ball 1.65 s · Ring 1.81 s. Spin share: 0%, 29%, 33%, 40%, 50%.
- Nothing changes. Mass and radius cancel out in a = g sin θ ÷ (1 + I/mr²): only the shape matters.
- Solid ball 5.29 m/s, ring 4.43 m/s. The ring puts half its energy into spinning, the solid ball only 2/7, so the ball has more left for moving along.
- mgh = ½mv² + ½Iω², with ω = v/r and I = kmr²: mgh = ½mv²(1 + k), so v = √(2gh ÷ (1 + k)).
- k = ½. v = √(2 × 9.8 × 2 ÷ 1.5) = √26.1 ≈ 5.1 m/s.
- a = g sin θ ÷ (1 + ⅖) = 9.8 × 0.5 ÷ 1.4 = 3.5 m/s².
- Friction at the contact point gives the torque that starts it spinning. When rolling without slipping, the contact point is momentarily at rest, so friction does no work and energy is conserved.
Free to print and share for teaching. Made with the interactive simulation at jugnix.com/simulations/rolling-torque.