Category: HC Verma Part 1: Mechanics

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A rotor starts from rest and reaches 300 rpm in 1 minute. Find the angular acceleration and the number of revolutions made. $\omega_f = 300 \times 2\pi/60 = 10\pi$ rad/s; $\alpha = \omega_f/t$; $N = \theta/(2\pi)$ Step 1: $\alpha = 10\pi/60 = \pi/6$ rad/s². Step…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A banked circular track has angle 20° and radius 100 m, $\mu_s = 0.4$. Find the maximum safe speed. ($g = 10$ m/s², $\tan20°=0.364$) $v_{max} = \sqrt{rg(\tan\theta+\mu_s)/(1-\mu_s\tan\theta)}$ Step 1: $v_{max}^2 = 100\times10\times\dfrac{0.364+0.4}{1-0.4\ Given Information See problem statement for all…

Problem Statement Solve the rotational mechanics problem: Solve the kinematics problem: A particle moves in a circle of radius 0.8 m at 3 rev/s. Find its speed and centripetal acceleration. $v = \omega r$; $a_c = v^2/r = \omega^2 r$ Step 1: $\omega = 3 \times 2\pi = 6\pi$ rad/s. Step 2: $v = 6\pi…

Problem Statement Find the radius of a geostationary orbit. ($M_E = 6\times10^{24}$ kg, $G = 6.67\times10^{-11}$, $T = 24$ h) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion,…

Problem Statement A particle rests on top of a smooth sphere of radius $R$. It is given a small push. Find the angle from the vertical at which it leaves the sphere. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement Solve the gravitation problem: Solve the gravitation problem: Find the period of a satellite orbiting just above Earth’s surface. ($g = 9.8$ m/s², $R_E = 6400$ km) $v = \sqrt{gR}$; $T = 2\pi R/v = 2\pi\sqrt{R/g}$ Step 1: $T = 2\pi\sqrt{R/g} = 2\pi\sqrt{6.4\times10^6/9.8} = 2\pi\sqrt{6.53\times10^5} = 2\pi \times 808 = 5077$ s $\a…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Earth (mass $6\times10^{24}$ kg) orbits the Sun at $r = 1.5\times10^{11}$ m with $T = 1$ year $= 3.15\times10^7$ s. Find the centripetal force on Earth. $F_c = m\omega^2 r = m(2\pi/T)^2 r$ Step 1: $\omega = 2\pi/(3.15\times10^7) =…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A flywheel of radius 0.3 m has angular acceleration 5 rad/s². A point on the rim has what linear (tangential) acceleration? $a_t = r\alpha$ Step 1: $a_t = r\alpha = 0.3 \times 5 = 1.5$ m/s². $$\boxed{a_t = 1.5\text{ m/s}^2}$$ Initial velocity $u$ (or $v_0$)…

Problem Statement A motorcycle rides on the inside of a vertical cylindrical wall (radius 10 m) without falling. If $\mu_s = 0.4$, find the minimum speed. ($g = 10$ m/s²) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A ball of mass 0.2 kg slides inside a spherical bowl of radius 0.4 m at constant speed 2 m/s. Find the normal force at the bottom of the bowl. ($g = 10$ m/s²) At bottom: $N – mg…