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

I=0:\quad a_0=\frac{(m_2-m_1)g}{m_1+m_2}>a,\quad \boxed{T_1,T_2\text{ ci-dessus}}

problems.proof.analysis

For $I=0$ the denominator decreases and the ideal Atwood acceleration is recovered. With $I>0$ , some energy rotates the pulley, reducing the linear acceleration.

problems.proof.pitfall. Do not set

T_1=T_2

for a pulley with nonzero moment of inertia; unequal tensions are needed to produce torque.