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0593_C08_fm Page 277 Monday, May 6, 2002 2:45 PM

Principles of Dynamics: Newton’s Laws and d’Alembert’s Principle 277

let S have radius r and angular speed Ω (a constant), and let B have length and mass
*
m. Let the inertia forces on B be replaced by a single force F passing through the mass
*
center G of B together with a couple with torque T . Determine the n , n , and n compo-
1
3
2
*
nents of F and T .
*
P8.12.2: See Problem P8.12.1. Determine the moments of all forces on B (including gravity
and inertia forces) about the attachment point O.
P8.12.3: See Problems P8.12.1 and P8.12.2. Repeat Problems P8.12.1 and P8.12.2 for angular
˙
speed Ω that is not constant but instead has a derivative Ω .
P8.12.4: Solve Problems P8.12.1 and P8.12.2 for the following data: Ω = 300 rpm, = 3 ft,
θ = 30°, r = 2 in., and m = 0.5 slug.
P8.12.5: Solve Problems P8.12.1 and P8.12.2 for the following data: Ω = 300 rpm, = 1 m,
θ = 30°, r = 5 cm, and m = 8 kg.

Section 8.13 The Rolling Circular Disk
P8.13.1: Consider the case of a circular disk rolling on a circle at a constant speed. Find
an expression for the radius ρ of the circle on which the center G moves. Express ρ in
terms of r, θ , φ ˙ O , ψ O .
O