Motion in a Plane
Class 11 Physics · Physics Part I · Chapter 3
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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.
Scalars and vectorsMultiplication of vectors by real numbersAddition and subtraction of vectorsResolution of vectors and analytical methodMotion in a plane with constant accelerationProjectile motionUniform circular motion
Key terms
Scalar
A physical quantity having only magnitude, specified completely by a number with a unit, e.g. mass or temperature.
Vector
A physical quantity having both magnitude and direction and obeying the laws of vector addition, e.g. velocity or force.
Resolution of a vector
The process of splitting a vector into components, usually along mutually perpendicular axes.
Projectile motion
The two-dimensional motion of a body thrown into the air, combining constant horizontal velocity with vertical free fall.
Centripetal acceleration
The acceleration of a body in uniform circular motion, of magnitude \(v^{2}/r\) directed toward the centre.
Angular speed
The rate of change of angular position, \(\omega=v/r\), measured in radians per second.
Extra questions & answers
Try one from this chapter
Which of the following is a vector quantity?