Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

derive relation between angular acceleration and linear acceleration  
Asked by singhparansh | 18 Dec, 2021, 05:15: PM
answered-by-expert Expert Answer
Let us consider a circular lemma as shown in fifure that rotates about an axis passing through centre of mass.
Let z-axis coincide with the axis of rotation so that lemma is in x-y plane.
 
At a point P , we see that tangential velocity vector begin mathsize 14px style v with rightwards arrow on top end style is mutually perpendicular to angular velocity vector begin mathsize 14px style omega with rightwards arrow on top end style
and radial position vector begin mathsize 14px style r with rightwards arrow on top end style .
If the lemma makes one complete rotation in T seconds , then linear displacement made by point P in tangential direction is ( 2π r )
 
Hence velocity v in tangential direction , v = ( 2π r ) / T
 
But angular velocity ω = 2π / T 
 
Hence from above two expressions, we get , v = ω r
 
Since magnitude of velocity v in tangential direction is produt of magnitude of angular velocity and radial distance
and also direction of velocity v is mutually perpendicular to vector begin mathsize 14px style r with rightwards arrow on top end style
and vector begin mathsize 14px style omega with rightwards arrow on top end style , then we get velocity vector begin mathsize 14px style v with rightwards arrow on top end style in terms of vector product as
begin mathsize 14px style v with rightwards arrow on top end style = begin mathsize 14px style omega with rightwards arrow on top end style × begin mathsize 14px style r with rightwards arrow on top end style
Acceleration begin mathsize 14px style a with rightwards arrow on top end style = ( d begin mathsize 14px style v with rightwards arrow on top end style / dt ) in tangential direction is determined by differentiating abvove expression .
begin mathsize 14px style fraction numerator d v with rightwards arrow on top over denominator d t end fraction space equals space fraction numerator d omega with rightwards arrow on top over denominator d t end fraction cross times r with bar on top space plus space space fraction numerator d r with rightwards arrow on top over denominator d t end fraction cross times space omega with rightwards arrow on top end style
since  ( dbegin mathsize 14px style r with rightwards arrow on top end style / dt )= 0 , we get begin mathsize 14px style fraction numerator d v with rightwards arrow on top over denominator d t end fraction space equals space fraction numerator d omega with rightwards arrow on top over denominator d t end fraction cross times r with bar on top space end style
where begin mathsize 14px style alpha with rightwards arrow on top end style = ( dbegin mathsize 14px style omega with rightwards arrow on top end style  / dt ) is angular acceleration.
Hence by magnitude ,  a = α r  is the relation between angular acceleration and acceleration in tangential direction .
Answered by Thiyagarajan K | 19 Dec, 2021, 09:47: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Physics
what type of image produced by plane mirror
Asked by agankitgupta938 | 18 Apr, 2024, 04:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
how is light made
Asked by infinityupgraded | 13 Apr, 2024, 08:17: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
what are the ray diagrams??
Asked by suryamr2019 | 08 Mar, 2024, 04:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
Plssss answer..... Assertion: Magnetic field lines never intersect each other. Reason: If they intersect, then at the point of intersection, the compass needle would point towards two directions, which is not possible.
Asked by sheetal.kolte | 04 Mar, 2024, 12:38: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
what is drawn
question image
Asked by shrilakshmimunoli | 01 Mar, 2024, 01:15: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
write ohm's law for electric circuit. Also write the necessary formula for this .
Asked by khajannirwan | 27 Feb, 2024, 10:20: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
where can i find a video on magnetic field in physics? thanks
Asked by sailakshmi.avinesh | 13 Feb, 2024, 07:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
find Req
question image
Asked by sakshikatewa0 | 08 Feb, 2024, 12:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
student observes the above phenomenon in the lab as a white light passes through a prism. Among many other colours, he observed the position of the two colours Red and Violet. What is the phenomenon called? What is the reason for the violet light to bend more than the red light?
Asked by saurabhjd527 | 30 Jan, 2024, 07:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Physics
Will a current carrying conductor produce an electric field?
Asked by saanviyadla | 24 Jan, 2024, 07:06: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×