Trigonometric Ratios for Compound Angles – Part2 Cosine of the Sum of Two Angles: for all angles A and B Proof: Let X’OX and YOY’ be the coordinate axes. Consider a unit circle with O as the center. Let P₁, P₂ and P₃ be the three points on the circle such that We know Read more about Trigonometric Ratios for Compound Angles – Part2[…]
Sticking of a Person with the Wall of Rotor A person with a mass m stands in contact against the wall of a cylindrical drum (rotor). The coefficient of friction between the wall and the clothing is . If rotor starts rotating about its axis, then person thrown away from the center due to centrifugal Read more about Sticking of a Person with the Wall of Rotor[…]
Trigonometric Ratios for Compound Angles – Part1 Cosine of the Difference of Two Angles: for all angles A and B Proof: Let X’OX and YOY’ be the coordinate axes. Consider a unit circle with O as the center. Let P₁, P₂ and P₃ be the three points on the circle such that We know Read more about Trigonometric Ratios for Compound Angles – Part1[…]
Impulse 1) When a large force works on a body for every small time interval, it is called as impulsive force. An impulsive force does not remain constant, but changes first from zero to maximum and then from maximum to zero. In such case we measure the total effect of force. 2) Impulsive of a Read more about Impulse[…]
Non Uniform Circular Motion If the speed of the particle in a horizontal circular motion changes with respect to time, then its motion is said to be non-uniform circular motion. Consider a particle describing a circular path of radius r with center at O. let at an instant the particle be at P and be Read more about Non Uniform Circular Motion[…]
Elementary Equations – Problems 1.Find the values of θ which satisfy rsinθ = 3 and r = 4 (1 + sinθ), 0 ≤ θ ≤ 2π. solution: rsinθ = 3 and r = 4 (1 + sinθ), 0 ≤ θ ≤ 2π rsinθ = 3 r = 3/sinθ 3/sinθ = 4 (1 + sinθ) 3 Read more about Elementary Equations – Problems[…]
Energy of Projectile A body which is in flight through the atmosphere under the effect of gravity alone and is not being propelled by any fuel is called projectile. If the force acting on a particle is oblique with initial velocity then the motion of particle is called projectile motion. When a projectile moves upwards Read more about Energy of Projectile[…]
General Solution of Some Standard Equations General solution of Equation sinθ = sinα: sinθ = sinα sinθ – sinα = 0, , , , , , θ + α = (2m + 1) π θ = (2m + 1) π – α, m ϵ Z ….(1) (θ – α)/2 = sin⁻¹(0) (θ – α)/2 = Read more about General Solution of Some Standard Equations[…]
Sticking of a Block with Accelerated Cart Acceleration of an object is defined as its rate of change of velocity at that instant. It is denoted as “a” and the units are. Any object experiencing an unbalanced force, constant or variable show acceleration (or) Any object undergoing a change in its velocity either magnitude or Read more about Sticking of a Block with Accelerated Cart[…]
Fundamental Laws of Logarithms- Part3 7. For a, n > 0 and a ≠ 1; Proof: Let . Then . Therefore, , Examples: (1) (2) (3) 8. , where a, n > 0, a ≠ 1 Proof: Let then, , , , , qx = yp, ⇒ x = (p/q)y, ⇒ . Example: What is Read more about Fundamental Laws of Logarithms- Part3[…]