Chapter 4 Solved Numericals: Turning Effect of Forces and Circular Motion

Interactive Study Notes Preview

Chapter Overview & SLOs

What is covered in these solved numericals? This section provides comprehensive step-by-step solutions to the numerical problems for Chapter 4, "Turning Effect of Forces and Circular Motion." The exercises focus on the practical application of rotational and circular dynamics. How do we calculate torque? You will learn to calculate torque (moment of force) acting on tools like spanners and wrenches: - Formula: $τ = F × d$ (torque = force × perpendicular distance from pivot called moment arm) - Units: Newton-meter (Nm) - Important conversions: Convert spanner length from cm to m before calculating torque (divide by 100) - Finding required arm length: For a given force and desired torque, $d = τ/F$ - Direction: Clockwise (negative) and anti-clockwise (positive) How do we apply the principle of moments? You will find detailed applications of the principle of moments to balance uniform bars and meter rods with multiple suspended masses: - Principle of moments: Sum of clockwise moments = Sum of anti-clockwise moments for rotational equilibrium - Balancing meter rods: Find unknown masses or positions in balanced systems - Weight of uniform rod: Acts at its center of gravity (midpoint for uniform rods) - Multiple suspended masses: Calculate each torque separately and set sum clockwise = sum anti-clockwise How do we calculate centripetal force? The notes include complex problems on circular motion: - Formula: $F_c = \frac{mv^2}{r}$ (centripetal force = mass × velocity² / radius) - Unit conversions: Convert velocity from km/h to m/s (multiply by 5/18 or divide by 3.6) - Finding radius: If diameter given, radius = diameter/2 - Examples: Car navigating a roundabout, object tied to string rotating in circle How do we calculate orbital speed of satellites? Students will master two methods for determining the orbital speed of geostationary satellites: - Method 1 (Gravitational approach): $v_o = \sqrt{\frac{GM}{r}}$ where G = gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²), M = Earth's mass (6 × 10²⁴ kg), r = distance from Earth's center (Earth's radius + height) - Method 2 (Period-radius relation): $v = \frac{2πr}{T}$ where T = orbital period. For geostationary satellites: T = 86400 seconds (24 hours) - Important values: Earth's radius = $6.4 × 10^6$ m (6400 km) - The two methods should give the same result when using consistent values These solutions emphasize the importance of identifying moment arms correctly, maintaining equilibrium through balanced torques, proper unit conversions, and using correct physical constants. They are strictly designed to help students master the mathematical requirements of the FBISE 2026 annual examination.

• How do we calculate torque and find required arm length? Calculate the torque produced by a force at a given moment arm using τ = F × d (convert cm to m by dividing by 100), and determine the required arm length for specific force applications using d = τ/F, with torque measured in Newton-meters (Nm).
• How do we apply the principle of moments to balanced systems? Apply the second condition of equilibrium (principle of moments: sum of clockwise moments = sum of anti-clockwise moments) to find unknown masses or positions in balanced systems, including uniform meter rods with multiple suspended masses, remembering that the weight of a uniform rod acts at its midpoint (center of gravity).
• How do we determine centripetal force for circular motion? Determine the centripetal force for objects in circular motion using Fc = mv²/r, relating mass (kg), velocity (m/s - convert from km/h by multiplying by 5/18), and radius of the path (m - if diameter given, radius = diameter/2), with force measured in Newtons (N).
• How do we calculate orbital speed of satellites? Calculate the orbital speed of satellites using two methods: the gravitational field approach (v_o = √(GM/r) with G = 6.67 × 10⁻¹¹ Nm²/kg², M = 6 × 10²⁴ kg, Earth's radius = 6.4 × 10⁶ m) and the circular motion period-radius relation (v = 2πr/T with T = 86400 seconds for geostationary satellites), ensuring both methods yield consistent results.

Frequently Asked Questions (FAQ)