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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A particle moves in the x-y plane according to rule x = a sin ωt and y = a cos ωt. The particle follows

  • an elliptical path

  • a circular path 

  • a parabolic path

  • a straight line path inclined equally to x and y- axes


B.

a circular path 

straight x space equals space straight a space sin space ωt space rightwards double arrow space straight x over straight a space equals space sin space ωt
straight x space equals space straight a space cos space ωt space rightwards double arrow space straight x over straight a squared space equals space cos space ωt
therefore space straight x squared over straight a squared space plus straight y squared over straight b squared space equals space 1
or space
straight x squared space plus space straight y squared space equals space straight a squared

This is the equation of a circle, so the particle follows a circular path.
straight x space equals space straight a space sin space ωt space rightwards double arrow space straight x over straight a space equals space sin space ωt
straight x space equals space straight a space cos space ωt space rightwards double arrow space straight x over straight a squared space equals space cos space ωt
therefore space straight x squared over straight a squared space plus straight y squared over straight b squared space equals space 1
or space
straight x squared space plus space straight y squared space equals space straight a squared

This is the equation of a circle, so the particle follows a circular path.
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Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Give three examples of scalar quantities.

Mass, temperature and energy
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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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