Question
For a particle in uniform circular motion the acceleration →a at a point P(R,θ)on the circle of radius R is (here θ is measured from the x-axis)
Answer: Option C
:
C
→r=Rcosθ^j
∴d→rdt=−Rsinθdθdt^i+Rcosθdθdt^j
⇒→v=−Rωsinθ^i+Rωcosθ^j
(asω=dθdtandd→rdt=→v)
⇒d→vdt=→a=Rωcosθdθdt^i+Rω(−sinθ)dθdt^j
⇒dsdt≡dθrdt=rdθdt=rω
∴ωordθdtisconstant
∴→v=−Rω2cosθ^i−Rω2sinθ^j
Substituting ω=vR
→a=−v2Rcosθ^i−−v2Rsinθ^j
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:
C
→r=Rcosθ^j
∴d→rdt=−Rsinθdθdt^i+Rcosθdθdt^j
⇒→v=−Rωsinθ^i+Rωcosθ^j
(asω=dθdtandd→rdt=→v)
⇒d→vdt=→a=Rωcosθdθdt^i+Rω(−sinθ)dθdt^j
⇒dsdt≡dθrdt=rdθdt=rω
∴ωordθdtisconstant
∴→v=−Rω2cosθ^i−Rω2sinθ^j
Substituting ω=vR
→a=−v2Rcosθ^i−−v2Rsinθ^j
Was this answer helpful ?
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