#angular velocity

A rod rotates at 10 rad/s in a 0.5 T field. If the length from the axis to the tip is 0.6 m, what is the emf induced?

**Energy stored in inductor** U =½ L I², L inductance, I current, energy in magnetic field, density u = B²/(2μ₀), B=μ₀ n I inside solenoid, U = (B²/2μ₀)×volume, illustrating equivalence of circuit and field energy. ε = (1/2) B ω R² . ε = (1/2) × 0.5 × 10 × (0.6)² = 0.9 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and U = ½ L I², result 0.9 V follows, reflecting Faraday's law and Lenz's opposition.

Ref: NCERT > Physics Book > Electromagnetic Induction > Self-Induction and Self-Inductance

View Details

AC Generator, Back EMF and Time Duration of EMF

A rod rotates at 25 rad/s in a 0.3 T field. If the length from the axis to the tip is 0.8 m, what is the emf induced?

**Back emf** in motor opposes applied voltage, e_b = N B A ω sin ωt, reduces net current, at start ω=0 e_b=0 current large, as speed increases e_b increases limiting current, power conversion mechanical, principle of motor and generator reciprocity. ε = (1/2) B ω R² . ε = (1/2) × 0.3 × 25 × (0.8)² = 2.4 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and U = ½ L I², result 2.4 V follows, reflecting Faraday's law and Lenz's opposition.

Ref: NCERT > Physics Book > Electromagnetic Induction > AC Generator, Back EMF and Time Duration of EMF

View Details

Rotational EMF and AC Generator

A rod rotates at 20 rad/s in a 0.4 T field. If the length from the axis to the tip is 0.5 m, what is the emf induced?

**Maximum emf** e₀ = N B A ω, for 180 turns A=0.02 m² B=0.03 T ω=60 rad/s, e₀=180×0.03×0.02×60=6.48 V, illustrating dependence on N, B, A, ω, used in generator design, increasing N or B or A or ω raises output. ε = (1/2) B ω R² . ε = (1/2) × 0.4 × 20 × (0.5)² = 5 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and U = ½ L I², result 5 V follows, reflecting Faraday's law and Lenz's opposition.

Ref: NCERT > Physics Book > Electromagnetic Induction > Rotational EMF and AC Generator

View Details

PHYSICS

The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions?

Given: The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions? These values define the system as per NCERT data. Formula: (a) [v / r] = [L T^{-1] / [L] = [T^{-1]. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: (b) [a t] = [L T^{-2] [T] = [L T^{-1] . (c) [F / m] = [M L T^{-2] / [M] = [L T^{-2] . (d) [s / t] = [L] / [T] = [L T^{-1] . (a) matches. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kgâ»Â¹ Kâ»Â¹, m/sÂ², 10â»âµ are properl

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

View Details

Moment of Inertia and Radius of Gyration

A wheel with moment of inertia 8kg m2 rotates at 2rad/s. A torque of 16Nm acts for 3s. What is its final angular velocit

α = τI = 168 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 2+6 = 8rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.