Two bicycle wheels are constructed from identical masses of metal wire
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Two bicycle wheels are constructed from identical masses of metal wire.
• Wheel A is built so that nearly all the mass is concentrated in a thin rim at radius R from the axle.
• Wheel B is built so that the same total mass is distributed uniformly among many very light spokes that extend radially from the axle out to the rim; the mass of the rim is negligible.
Both wheels are spun up to the same constant angular speed before being released to spin freely in mid-air.
Answer the following questions. Assume each wheel can be treated as a single rigid object and neglect air resistance.
(a) Describe qualitatively which wheel has the greater magnitude of angular momentum at the instant they are released, or whether the magnitudes are the same. Base your answer on appropriate physical reasoning.
(b) Without performing numerical calculations, explain how the distribution of mass in each wheel leads to the conclusion reached in part (a). In your explanation, refer explicitly to relevant physical quantities.
(c) Suppose the wheels are instead spun so that their angular momenta have equal magnitudes when released. Describe how the required angular speed of Wheel A would compare with that of Wheel B and justify your answer.