How Do You Calculate Angular Velocity at Maximum Height in Projectile Motion?

[Draco27]

Homework Statement

We need to find angular velocity of a particle from point of launch at its maximum height. Particle is launched at θ angle wrt horizontal. Initial velocity is u. Only acceleration is gravity.

Homework Equations

All projectile equations i suppose ( h(max)=u²sin²/2g , range= u²sin2θ/g etc) and of angular velocity ( v=ωXr)

The Attempt at a Solution

I suppose angular velocity is w_° at initial. So, if i could get angular acceleration and then use ω=ω_° + αt as at max height, i suppose angular velocity is 0 { same direction of both velocity and distance vectors, so θ = 0°}

some help??

 

[cepheid]

It seems easy enough to find θ vs. time given the trajectory, and then to say that ω = dθ/dt, assuming that you know what a derivative is.

 

[Draco27]

yes i know about derivative.

but how do i plot that theta vs time graph??

 

[haruspex]

I suppose angular velocity is w_° at initial. So, if i could get angular acceleration and then use ω=ω_° + αt

That would assume the angular acceleration is constant, which it probably is not.

as at max height, i suppose angular velocity is 0

What do you think the question means by angular velocity? It says "from the point of launch", so I think it means dθ/dt, where θ is the angle it subtends from its current position to the horizontal at the launch point. If so, it won't be zero at max height.
Can you try writing its equations of motion in polar, origin at launch point?

 

[Draco27]

you mean that of trajectory??

if yes, then i know that eqn. But what do i do with that equation??also forget what i attempted. i got it all wrong...

also if i were to find angular acceleration as a function of sth, how would i do that??

 

[haruspex]

you mean that of trajectory??

if yes, then i know that eqn. But what do i do with that equation??

Then please post your working: equations of motion in Cartesian using the launch point as origin, then converted to polar form.

 

[Draco27]

guys someone please help...

a good person above asked me to post some equations but i have no idea which equations i need to post...if basic projectile equations are required, (that of range and velocity and max height, ) here they arerange =[( u*sin {theta})^2]/2*g

max height= [u^2 *sin[2*theta}]/g

for velocity, we change the vertical component by eqn v=u-gt and take vector sum of horizontal and vertical components...

angular velocity : no idea

angular acceleration : no idea...

 

[haruspex]

By equations of trajectory, I mean the equations that tell you where the particle will be (x and y coordinates, say) at some time t after launch. I'm sure you know such equations, but you have not posted them yet.

 

[Draco27]

you mean this ? y= x*tan[theta] - (x^2)*g/(2*{u^2}*cos^2[theta])

this is independent of time...

in single directions, along horizontal direction s= u*cos{theta}*t

along vertical direction s = u*sin[theta]*t - (g*t^2)/2

 

[haruspex]

in single directions, along horizontal direction s= u*cos{theta}*t
along vertical direction s = u*sin[theta]*t - (g*t^2)/2

Good, but to make it clearer, we'll write those as x=, y=...
When at the point (x, y), what is the angle subtended to the horizontal at the launch point?

 

[Draco27]

i think arctan(y/x)

 

[Draco27]

any help??

 

[mukundpa]

Can we calculate angular momentum of the particle about the launch point at the highest point? I think in that case to calculate the angular velocity will be easy.