Related Formula
θ = ((ω₁ + ω₂)/(2)) t$$\theta = \left(\frac{\omega_1 + \omega_2}{2}\right) t$$
N = (θ)/(2π)$$N = \frac{\theta}{2\pi}$$
Core Logic
ω₁ = 600 × (2π)/(60) = 20π rad/s$$\omega_1 = 600 \times \frac{2\pi}{60} = 20\pi \text{ rad/s}$$
ω₂ = 1200 × (2π)/(60) = 40π rad/s$$\omega_2 = 1200 \times \frac{2\pi}{60} = 40\pi \text{ rad/s}$$
α = (40π - 20π)/(10) = 2π rad/s²$$\alpha = \frac{40\pi - 20\pi}{10} = 2\pi \text{ rad/s}^2$$
θ = (20π)(10) + (1)/(2)(2π)(10)² = 300π rad$$\theta = (20\pi)(10) + \frac{1}{2}(2\pi)(10)^2 = 300\pi \text{ rad}$$
N = (300π)/(2π) = 150$$N = \frac{300\pi}{2\pi} = 150$$
Alternatively, average rpm = (600+1200)/(2) = 900 rpm = 15 rps ⇒ N = 15 × 10 = 150$= \frac{600+1200}{2} = 900\text{ rpm} = 15\text{ rps} \Rightarrow N = 15 \times 10 = 150$.
Pattern Recognition
Average angular velocity multiplied by time gives total revolutions.
Chapter Mix
Class 11 Physics: System of Particles and Rotational Motion