If angular momentum is conserved, an increase in moment of inertia results in a decrease in angular velocity, and vice versa.

Angular momentum L = Iω; if L is doubled and I remains constant, ω must also double.

If angular momentum is conserved, it implies that the net external torque acting on the system is zero.

Angular momentum is conserved when the net external torque acting on the system is zero.

Zero angular momentum does not imply rest; it can be in linear motion.

Zero angular momentum implies no net rotation; particles can still move linearly.

Centripetal acceleration (a_c) = ω²r. If ω is doubled, a_c becomes (2ω)²r = 4ω²r.

Area = πr². 154 = (22/7)r². Solving gives r² = 154 * 7 / 22 = 49, so r = 7 cm.

Area = πr^2 => 36π = πr^2 => r^2 = 36 => r = 6.

Area = πr^2 => 50π = πr^2 => r^2 = 50 => r = √50 = 5√2.

Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.

Magnetic flux (Φ) is given by the product of magnetic field (B) and area (A). If the area is doubled and the magnetic field remains constant, the magnetic flux also doubles.

Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled and the magnetic field (B) remains constant, the magnetic flux also doubles.

Magnetic flux (Φ) is given by Φ = B * A. If the area (A) is doubled, the magnetic flux also doubles.

Magnetic flux Φ is given by Φ = B * A. If the area A is doubled while B remains constant, the magnetic flux also doubles.

Induced EMF is proportional to the area of the loop. If the area is doubled, the induced EMF also doubles.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.

If the height of a parallelogram is halved, the area is also halved, as area = base × height.

This formula applies to a kite, where the diagonals intersect at an angle.

In the formula for the area of a quadrilateral, d1 and d2 represent the lengths of the diagonals.

Area = Length * Width. Therefore, Width = Area / Length = 48 / 8 = 6 meters.

Area = Length × Width. Therefore, Width = Area / Length = 48 / 8 = 6 units.

Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.

Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(10)². Solving gives θ = 90 degrees.

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(5)². Solving gives θ = 90°.

Area of a sector = (θ/360) × πr². Thus, 30 = (θ/360) × π × 25. Solving gives θ = (30 × 360)/(25π) ≈ 72°.

Area of a square = side². Therefore, side = √64 = 8 cm.

Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.

Area = (1/2) × (base1 + base2) × height. Thus, 60 = (1/2) × (10 + 20) × height, giving height = 60 / 15 = 4 units.