Problem 1

Two small masses

m_1

and

m_2

are joined by a light inextensible string over a fixed pulley of radius

R

and moment of inertia

I

with a frictionless axle;

m_2>m_1

. The string does not slip, both segments are vertical, and the string's mass is negligible. Release from rest and take

g=9.8\,\mathrm{m/s^2}

. (a) Find the acceleration and pulley angular acceleration. (b) Find the tension in each segment. (c) Find the acceleration for a massless pulley and explain how it compares with the inertial pulley.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

a=\frac{(m_2-m_1)g}{m_1+m_2+I/R^2},\qquad \alpha=\frac aR

problems.proof.analysis

Add the two Newton equations, replace the tension difference by $Ia/R^2$ , and solve for $a$ . The denominator includes both masses and the pulley inertia referred to the string.