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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane4 Marks
Question
Read the passage given below and answer the following questions from $i$ to $v.$ When an object follows a circular path at a constant speed, the motion of the object is called uniform circular motion. The word “uniform” refers to the speed, which is uniform (constant) throughout the motion. Suppose an object is moving with uniform speed $v$ in a circle of radius $R$ Since the velocity of the object is changing continuously in direction, the object undergoes acceleration. Let us find the magnitude and the direction of this acceleration. Thus, the acceleration of an object moving with speed v in a circle of radius $R$ has a magnitude $V^2/R$ and is always directed towards the centre. This is why this acceleration is called centripetal acceleration (a term proposed by Newton). A thorough analysis of centripetal acceleration was first published in $1673$ by the Dutch scientist Christiaan Huygens $(1629-1695)$ but it was probably known to Newton also some years earlier. “Centripetal” comes from a Greek term which means ‘centre-seeking’. Since $v$ and $R$ are constant, the magnitude of the centripetal acceleration is also constant. However, the direction changes pointing always towards the centre. Therefore, a centripetal acceleration is not a constant vector. We can express centripetal acceleration ac in terms of angular speed as $\text{a}_\text{c}=\omega^2\text{R}$ The time taken by an object to make one revolution is known as its time period T and the number of revolution made in one second is called its frequency $v (=1/T).$ However, during this time the distance moved by the object is $\text{s}=2\pi\text{R}.$ Therefore, $\text{v}=2\pi\frac{\text{R}}{\text{T}}=2\pi\text{ Rv}$ In terms of frequency n, we have $\omega=2\pi\text{v}$
$\text{V}=2\pi\text{ RV}$
$\text{ac}=4\pi^2\text{v}^2\text{R}$
  1. SI unit of angular velocity is
  1. Rev/ sec
  2. $m/ s$
  3. $m/ s^2$ 
  4. None of these
  1. A centripetal acceleration is not a constant vector. True or false?
  1. True
  2. False
  1. Define Uniform circular motion
  2. What is meaning of word centripetal?
  3. What is centripetal acceleration? Give its relation with angular velocity
✓

Answer

  1. (a) Rev/ sec
  2. (a) True
  3. When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.
  4. “Centripetal” comes from a Greek term which means ‘centre-seeking’ i.e. always directed towards centre of a circle.
  5. Acceleration of particle performing uniform circular motion which is always directed towards centre of a circle is called centripetal acceleration. We can express centripetal acceleration ac in terms of angular speed as.
$\omega=2\pi\text{v}$
However, during this time the distance moved by the object is $s = 2\pi R.$ In terms of frequency V, we have
$\omega=2\pi\text{v}$
$\text{V}=2\pi\text{ RV}$
$\text{ac}=4\pi^2\text{v}^2\text{R}$

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