A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25π Nm for 40 seconds, the speed increases to 2100 rpm. What is the diameter of the disk?
🌀 Rotating Disk Problem – Explained with Concept & Calculation ❓ Problem Statement: A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25π Nm for 40 seconds , the speed increases to 2100 rpm . What is the diameter of the disk? ⚙️ Step-by-Step Conceptual Breakdown To solve this, we’ll use rotational motion concepts : 🧮 Key Equations Involved: Torque and Angular Acceleration: τ = I α Where: τ \tau = torque, I I = moment of inertia of disk = 1 2 M R 2 \frac{1}{2}MR^2 , α \alpha = angular acceleration Angular Velocity: Convert RPM to rad/s: ω = 2 π ⋅ RPM 60 Angular Kinematics: ω f = ω i + α t 🧾 Given: Mass of disk, M = 1 kg M = 1 \, \text{kg} Initial speed, ω i = 1800 rpm = 2 π × 1800 60 = 60 π rad/s Final speed, ω f = 2100 rpm = 2 π × 2100 60 = 70 π rad/s \omega_f = 2100 \, \text{rpm} = \frac{2\pi \times 2100}{60} = 70\pi \, \text{rad/s} Ti...