Question

A rope is wrapped around a pulley many times. The pulley can be modeled as a solid disk of radius R and mass M, and a mass mA hangs vertically from the pulley. The mass is released from rest. show answer Incorrect Answer 25% Part (a) What is the magnitude of the tangential acceleration of the hanging mass?

Answer 1

The magnitude of the tangential acceleration of the hanging mass is 2mg/MR

Tangential acceleration of the hanging mass

The tangential acceleration of the hanging mass around the pulley is determined from the principle of conservation of angular momentum as shown below;

τ = Iα

Where;

• I is the moment of inertia
• α is the angular velocity

$\alpha = \frac{\tau}{I} \\\\\alpha = \frac{mgR}{3/2MR^2} \\\\\alpha = \frac{2mgR}{3MR^2} \\\\\alpha = \frac{2mg}{3MR}$

Where;

• m is the hanging mass
• M is the mass of solid disk

The tangential acceleration is calculated as follows;

$a = \alpha R\\\\a = \frac{2mg}{3MR} \times R\\\\a = \frac{2mg}{3M}$

Thus, the magnitude of the tangential acceleration of the hanging mass is 2mg/MR

Learn more about tangential acceleration here: brainly.com/question/11476496