# Treating a projectile like a rotational system?

## Homework Statement

A projectile of mass m is fired from ground level with speed v0 and at angle ##\theta## with respect to the horizontal. Basically there is a projectile from start to finish, with an pivot starting at the x coordinate for the highest point on the projectile. The teacher wants us to find the net torque vector, angular velocity vector, moment of inertia, and angular momentum vectors.

## The Attempt at a Solution

I have trouble understanding how projectile motions can even be looked at like a rotational system. To me, the only force ever acting is gravity, but then the projectile is rotating around the origin, so shouldn't that mean that there's also another torque force?

If the only force is g, then the torque would be mgr (r is the distance from the pivot) at the start point and then 0 at the top (since the g force is towards the pivot so no force done)? Also why does the teacher emphasize looking for the torque VECTOR? Does that mean that it's point towards us?

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jedishrfu
Mentor
Welcome to PF!

Is this problem in reference to orbiting the Earth ?

Nope! It's literally just a projectile (an object being thrown) and then treated like a rotational system.

Delta2
Homework Helper
Gold Member
You consider the earth ground as an infinite plane with gravity vector vertical to it or you treat the earth ground as spherical and the gravity vector in the radial direction?

jedishrfu
Nidum
Gold Member
Is this just the standard projectile problem but to be solved using polar coordinates instead of the more commonly used Cartesian coordinates ?

The former.

jedishrfu
Mentor
The problem does state that its being launched horizontally (zero degrees to the horizontal) right?

The problem does state that its being launched horizontally (zero degrees to the horizontal) right?
No! It's being launched at an angle (like 45 degrees or something)!!

jedishrfu
Mentor
No! It's being launched at an angle (like 45 degrees or something)!!

A projectile of mass m is fired from ground level with speed v0 and at angle -0- with respect to the horizontal. Basically there is a projectile from start to finish, with an pivot starting at the x coordinate for the highest point on the projectile. The teacher wants us to find the net torque vector, angular velocity vector, moment of inertia, and angular momentum vectors. ???

Sorry haha what i was trying to do was make the theta sign, but I guess it looks like a 0, sorry. The angle is assumed to be non zero though.

jedishrfu
Mentor
Okay so the projectile is launched at some angle from x=0 and y=0 into the air and gravity pulls on it so that it will follow a parabolic path.

That curved path implies that it has angular momentum so do you know how to compute its angular momentum vectorially?

So you agree that the only force for the torque is the graviity?

So the torque can be computed by Fr?? and is mgr at the (0,0) and is 0 at the peak?

jedishrfu
Mentor
Isn't torque defined as T = r x F ?

Isn't torque defined as T = r x F ?
Isn;t that what i wrote?

jedishrfu
Mentor
Torque is a vector quantity and you use the r x F to compute it, the magnitude of T is ## |T| = |r| |F| sin \theta## where ##\theta## is the angle between r and F and the direction of the torque follows the righthand rule from r to F and the righthand thumb points in the direction of T.

What would be the torque vector in this case given the information.

I think mgr, and can;t think of any other possibility. Please give your insight? :)

jedishrfu
Mentor
Yes, I reread your problem and I think you're right as the pivot point is the x value of where the particle is highest and y=0 so you'd use it to compute the torque but since the force is parallel to the r vector then the torque magnitude is zero at that point.

jedishrfu
Mentor
Perhaps @Doc Al can add more to the discussion here as my physics is somewhat rusty.

Doc Al
Mentor
A projectile of mass m is fired from ground level with speed v0 and at angle θθ\theta with respect to the horizontal. Basically there is a projectile from start to finish, with an pivot starting at the x coordinate for the highest point on the projectile.
OK. I'll interpret that, like jedishrfu did, as wanting you to use that point on the ground directly under the projectile when it's at max height as your reference point for your calculations.

The teacher wants us to find the net torque vector, angular velocity vector, moment of inertia, and angular momentum vectors.
Good. You should know the definitions of those quantities.

I have trouble understanding how projectile motions can even be looked at like a rotational system. To me, the only force ever acting is gravity, but then the projectile is rotating around the origin, so shouldn't that mean that there's also another torque force?
The only force is gravity. Note that we are not talking about the projectile rotating about its center, but just ordinary projectile motion. (Think of it as a point mass-- a ball, perhaps.) And further realize that a point mass can have angular momentum and rotational inertia about some point as well as be subject to a torque about that point.

If the only force is g, then the torque would be mgr (r is the distance from the pivot) at the start point and then 0 at the top (since the g force is towards the pivot so no force done)?
Yes, the torque is zero at the top. The force (gravity) doesn't change as the projectile moves, but the torque does.

Also why does the teacher emphasize looking for the torque VECTOR?
To make sure you understand the concept!

Does that mean that it's point towards us?
At what point in the projectile's motion? (Compare the direction of the torque vector before and after the projectile reaches the highest point.)