CBSE Class 11 — Notes, Chapters & Practice Quizzes

Chapter 3: Motion in a Plane

Summary

To describe motion in two or three dimensions we need vectors, quantities having both magnitude and direction, as opposed to scalars which have magnitude only. Vectors are added by the triangle or parallelogram law and can be multiplied by a scalar. A vector is conveniently handled by resolving it into rectangular components along chosen axes; the analytical method of addition then adds components separately. Position, displacement, velocity and acceleration in a plane are all vectors, with velocity tangent to the path. For motion with constant acceleration the kinematic equations apply to each component independently. Projectile motion is treated as a combination of uniform horizontal motion and uniformly accelerated vertical motion under gravity; its path is a parabola, and expressions are derived for time of flight \(T=2v_0\sin\theta/g\), maximum height \(H=v_0^{2}\sin^{2}\theta/2g\) and horizontal range \(R=v_0^{2}\sin2\theta/g\), the range being maximum at a projection angle of 45 degrees. Uniform circular motion, in which speed is constant but direction changes, has a centripetal acceleration \(a_c=v^{2}/r=\omega^{2}r\) directed toward the centre, where \(\omega\) is the angular speed.

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