Category: HC Verma Part 1: Mechanics

Problem Statement A bead of mass 50 g is threaded on a smooth wire and rotates at $\omega = 4$ rad/s. The wire is horizontal at radius $r = 0.5$ m from the axis. Find the normal force from the wire. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement Solve the rotational mechanics problem: Solve the kinematics problem: A wheel starts from rest with angular acceleration $\alpha = 3$ rad/s². Find the angular displacement in 4 s and the angular velocity at that time. $\omega = \alpha t$; $\theta = \frac{1}{2}\alpha t^2$ Step 1: $\omega = 3 \times 4 = 12$ rad/s.…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Distinguish between centripetal force and centrifugal force. Which is real and which is pseudo? Centripetal: real force directed toward center (inertial frame); Centrifugal: pseudo force in rotating frame Centripetal force: A real force (could be tension, Given Information See…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A banked curve of radius 50 m is banked at 15°. Find the design speed at which no friction is needed. ($g = 10$ m/s²) $v = \sqrt{rg\tan\theta}$ Step 1: $v = \sqrt{50 \times 10 \times \tan15°} = \sqrt{500…

Problem Statement A conical pendulum has a string of length $L = 1$ m making 30° with the vertical. Find the period. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental…

Problem Statement A car of mass 800 kg goes through a loop (radius 10 m) at the inside top of the loop at 12 m/s. Find the normal force at the top. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A ball of mass 0.3 kg on a string of length 1.5 m moves in a vertical circle at minimum speed. Find the tension at the bottom. ($g = 10$ m/s²) See problem statement for all given quantities. Newton’s…

Problem Statement Solve the kinematics problem: Find the minimum speed at the bottom of a vertical circle (radius $r$) needed to complete the loop. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws on fundamental physical principles. The key is to ide Given…

Problem Statement Solve the kinematics problem: Find the minimum speed at the top of a vertical circular loop (radius 2 m) for a ball on a string to maintain tension. ($g = 10$ m/s²) All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) This problem draws…

Problem Statement Solve the kinematics problem: A ball on a string (length 1 m, mass 0.5 kg) is whirled in a vertical circle with speed 5 m/s at the bottom. Find the speed at the top using energy conservation. ($g = 10$ m/s²) All quantities, constants, and constraints stated in the problem above Physical constants…