Treating a projectile like a rotational system?

Tags:
1. May 24, 2016

LiliPling

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

Last edited by a moderator: May 24, 2016
2. May 24, 2016

Staff: Mentor

Welcome to PF!

Is this problem in reference to orbiting the Earth ?

3. May 24, 2016

LiliPling

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

4. May 24, 2016

Delta²

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?

5. May 24, 2016

Nidum

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

6. May 24, 2016

LiliPling

The former.

7. May 24, 2016

Staff: Mentor

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

8. May 24, 2016

LiliPling

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

9. May 24, 2016

Staff: Mentor

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. ???

10. May 24, 2016

LiliPling

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.

11. May 24, 2016

Staff: 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?

12. May 24, 2016

LiliPling

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?

13. May 24, 2016

Staff: Mentor

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

14. May 24, 2016

LiliPling

Isn;t that what i wrote?

15. May 24, 2016

Staff: 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.

16. May 24, 2016

LiliPling

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? :)

17. May 24, 2016

Staff: 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.

18. May 24, 2016

Staff: Mentor

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

19. May 24, 2016

Staff: Mentor

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.

Good. You should know the definitions of those quantities.

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.

Yes, the torque is zero at the top. The force (gravity) doesn't change as the projectile moves, but the torque does.

To make sure you understand the concept!

At what point in the projectile's motion? (Compare the direction of the torque vector before and after the projectile reaches the highest point.)