Irodov Problem 1.154 – Particle on Rotating Radius Vector

Problem Statement

The moment of inertia of a body about an axis is I and it rotates with angular momentum L. A torque N is applied. Find the angular acceleration.

Given Information

• Moment of inertia I
• Torque N

Physical Concepts & Formulas

$$N=I\beta,\quad \beta=N/I$$

Step-by-Step Solution

Step 1: Newton’s second law for rotation: N = Iβ.

Step 2: β = N/I.

Step 3: Angular velocity after time t: ω = ω₀ + βt = ω₀ + Nt/I.

Worked Calculation

β = N/I

Answer

$$\boxed{\beta=\frac{N}{I}}$$

Physical Interpretation

This is the rotational analog of Newton’s second law. A larger torque or smaller moment of inertia gives faster angular acceleration.