Rotational dynamics about a fixed axis: A very thin uniform rod, 2.40 m long and of weight 135 N, has a frictionless hinge at its lower end. It starts out vertically from rest and falls, pivoting about the hinge. Just as it has rotated through an angle of 55.0°, what is the downward acceleration of the end farthest from the hinge? A) 5.02 m/s² B) 8.03 m/s² C) 9.80 m/s² D) 12.0 m/s² E) 19.6 m/s²

Question

Quizplus · Accepted Answer

The downward acceleration of the end farthest from the hinge can be found using the formula for angular acceleration and the relationship between linear and angular acceleration. The angular acceleration is given by α = (3/2) * g * sin(θ) / L, where g is the acceleration due to gravity, θ is the angle, and L is the length of the rod. The linear acceleration a = α * L. Substituting the given values, the downward acceleration is approximately 12.0 m/s².

Rotational Dynamics About a Fixed Axis: a Very Thin Uniform