What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Distinguish a scalar from a vector.

A scalar has magnitude only; a vector has both magnitude and direction and adds according to the laws of vector addition.

State the parallelogram law of vector addition.

If two vectors are represented by adjacent sides of a parallelogram drawn from a point, their resultant is the diagonal through that point.

Why is resolution of a vector useful?

Resolving a vector into perpendicular components lets each component be handled independently using simple algebra.

Why is projectile motion analysed as two separate motions?

Because the horizontal and vertical motions are independent — uniform velocity horizontally and uniform acceleration \(g\) vertically.

What is the shape of the trajectory of a projectile?

A parabola, given by \(y=x\tan\theta-\tfrac{g x^{2}}{2v_0^{2}\cos^{2}\theta}\).

Write the formula for the horizontal range of a projectile.

\(R=\dfrac{v_0^{2}\sin2\theta}{g}\), which is maximum when the projection angle is 45 degrees.

Write the time of flight and maximum height of a projectile.

\(T=\dfrac{2v_0\sin\theta}{g}\) and \(H=\dfrac{v_0^{2}\sin^{2}\theta}{2g}\).

Define centripetal acceleration.

The acceleration directed toward the centre of a circular path, magnitude \(a_c=v^{2}/r=\omega^{2}r\), arising from the continuous change in the direction of velocity.

In uniform circular motion, why is there acceleration even though speed is constant?

Because velocity is a vector whose direction changes continuously, so the body is accelerated even though its speed is unchanged.

Relate linear speed and angular speed.

\(v=\omega r\), where \(\omega\) is the angular speed and \(r\) the radius of the circular path.

Motion in a Plane

Class 11 Physics · Physics Part I · Chapter 3

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CBSE Class 11 · Physics

Every formula of Ch 1–7, with page numbers

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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?

Flashcards & interactive practice