A horizontal wheel-and-axle system is mounted so it can rotate freely about a…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A horizontal wheel-and-axle system is mounted so it can rotate freely about a vertical axis through its center. Four identical spokes extend radially outward, and a small platform is attached to the end of each spoke at radius R=1.5m. Initially, four blocks each of mass m=2.0kg are placed, one on each platform, so that the wheel is in rotational equilibrium (at rest). A student then removes one block and places it on the diametrically opposite platform, doubling the mass on that platform and leaving one platform empty.
The axle is assumed frictionless, and air resistance is negligible.
(1) Part 1: Explain qualitatively whether the wheel will begin to rotate after the block is moved. Justify your answer in terms of net torque about the axle.
(2) Part 2: Derive a general condition relating the masses on the four platforms that must be satisfied for the wheel to remain in rotational equilibrium when masses are redistributed.
(3) Part 3: Suppose the student wants to restore equilibrium using only the three remaining blocks (no additional masses allowed) by repositioning them at radii r1, r2, and r3 (all ≤R) on their respective spokes. Develop one set of distances r1, r2, and r3 that will keep the wheel at rest, and demonstrate quantitatively that your choice satisfies the condition from part (b).