During a class discussion on the first law in translational and rotational form, three students make the following claims about a rigid wheel mounted on a frictionless axle.
Student A: “Because there is no net force on the wheel’s center of mass, its angular velocity must be constant.”
Student B: “If the net torque on the wheel is zero, its center of mass cannot accelerate.”
Student C: “A non-zero net force can exist while the net torque is zero, but in that case the wheel’s angular velocity will still be constant.”
Analyze these statements.
(1) Identify which student statements, if any, are incorrect.
(2) For each incorrect statement, provide a corrected version that is always true for a rigid body.
(3) Explain, using Newton’s first law in both translational and rotational form, why the corrected statements are valid. Your answer should explicitly reference the independence of translational and rotational equilibrium.