A solid cylinder of mass 5.2 kg and radius 6.4 cm is yoked to a spring. To be pr

Question

A solid cylinder of mass 5.2 kg and radius 6.4 cm is yoked to a spring. To be precise, the axle of the cylinder is attached to a horizontal spring of force constant 971.4 N/m. The cylinder rolls back and forth on a horizontal base with- out slipping. For simplicity, assume that the spring, the axle and the yoke which connects
them have negligible masses compared to the cylinder itself.
a) What is the angular frequency of the cylinder rolling back and forth around the equlib-
rium position?
Answer in units of s-1

Explanation / Answer

Take torque about contact of cylinder and surface. I = 3/2 M R^2 by the parallel axis theorem L(torque) = k x R torque about point of contact I a / R = -k x R since a/R = angular acceleration 3/2 m R a = - k x R d^2 x / dt^2 + 2 k /(3 m) = 0 Compare this to the equation for simple harmonic motion d^2 x / dt^2 + k x / m = 0 Since the angular frequency for SHM is (k/m)^1/2 the angular frequency must be (2 k /(3 m))^1/2

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