A particle is located at 3 m- 4 m and moving with v- 4- -3 - m-s- Find its magnitude of angular velocity about origin at this instant in rad-sec

ω = component of velocity perpendicular to r/r r=3î+4ĵ nbsp; v=4î 3ĵ Since, r·v =0 ∴v⊥r ∴ω =v/r =1 rad/s v= | v| =5 m/s ...

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Standard XII

Physics

Non Uniform Motion & Avg Velocity

A particle is...

Question

A particle is located at $(3 m, 4 m)$ and moving with $\to v = (4^i - 3^j) m / s .$ Find its magnitude of angular velocity about origin at this instant in rad/sec

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Solution

$ω = \frac{c o m p o n e n t o f v e l o c i t y p e r p e n d i c u l a r t o \to r}{r}$
$\to r = 3^i + 4^j$
$\to v = 4^i - 3^j$
Since, $\to r \cdot \to v = 0$
$∴ \to v ⊥ \to r$
$∴ ω = \frac{v}{r} = 1 r a d / s$
$v = ∣ ∣ \to v ∣ ∣ = 5 m / s$
$r = ∣ ∣ \to r ∣ ∣ = 5 m$
From the figure, we can see that $\to ω$ is along negative z-axis

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A particle is located at (3m,4m) and moving with →v=(4^i−3^j)m/s. Find its magnitude of angular velocity about origin at this instant in rad/sec

ω=componentofvelocityperpendicularto→rr→r=3^i+4^j →v=4^i−3^jSince, →r⋅→v=0∴→v⊥→r∴ω=vr=1rad/sv=∣∣→v∣∣=5m/sr=∣∣→r∣∣=5mFrom the figure, we can see that →ω is along negative z-axis

A particle is located at $(3 m, 4 m)$ and moving with $\to v = (4^i - 3^j) m / s .$ Find its magnitude of angular velocity about origin at this instant in rad/sec