A uniform disc of radius rests on a horizontal surface
PHYSICS · Multi-part · AP · Physics C: Mechanics · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A 1.0kg uniform disc of radius 0.15m rests on a horizontal surface. A light, non-stretching string is wound around the rim of the disc and pulled horizontally with a constant 5.0N force, causing the disc to accelerate without slipping. The disc’s moment of inertia about its central axis is I=21Mr2. Assume the only horizontal forces acting are the pull of the string and static friction.
(a) Determine the magnitude of the linear acceleration of the disc’s center of mass.
(b) Calculate the disc’s angular acceleration.
(c) Find the magnitude and direction (relative to the direction of motion of the center of mass) of the static friction force acting on the disc.
(d) Suppose instead the string were pulled upward at 30∘ above the horizontal with the same 5.0N tension. Without doing further calculations, state qualitatively whether the magnitude of the required static friction force would increase, decrease, or remain the same, and justify your reasoning.