Question

projectile path 5. ध्रुवीय नियामकों के पदों में एक कण का त्वरण ज्ञात कीजिए। Find the acceleration of a particle in terms of polar co-ordinates।..​

Answer 1

Answer:

l hope my answer is right

Answer 2

To find the radial and transverse velocity and acceleration for a particle with polar coordinates r=et and θ=t

Therefore let r–=r^––et and θ–=θ^––t

∴r–˙=ddt(r^––)et+ddt(et)r^––

Butr^––=cosθi^–+sinθj^–

∴r–˙=dθdtddθ(cosθi^–+sinθj^–)et+etr^––

=(−sinθi^–+cosθj^–)et+etr^––

∴r^––=etθ^––+etr^––

This is the particles velocity, the acceleration is given by:

r–¨=ddt(θ^––et+r^––et)

=ddt(θ^––)et+ddt(et)θ^––+ddt(r^––)et+ddt(et)r^––

=dθdtddθ(−sinθi^–+cosθj^–)et+etθ^––+etθ^––+etr^––

=−etr^––+etθ^––+etθ^––+etr^––

=2etθ^––

This is an acceleration in the transverse direction. But if θ=t and r=et then why do I get an acceleration in the transverse direction, and not the radial direction? Is the transverse velocity not constant