Projectile motion and angular motion

[abdul]

Hi.

I have two questions which I have been pondering on and I just can't figure it out. Maybe someone could be kind enough to answer the questions?

Q1; Projectile motion: Let's say we dropped a ball from a height called h.
We achieve a velocity $$v=\sqrt{2gh}$$. Let's then say that we hit the ball in differently angle with a paddle. What will the motion equations become?

Q2: Angular motion: Let's say we have a ball in vaacum. We make this ball rotate. Then this ball achieves angular velocity, the direction of the angular velocity $$\omega$$ can be found by the right-hand rule. But I am confused, what does the angular velocity's direction tell us? It it where the ball will move towards?

Thank you.

 

[dextercioby]

Hi.

I have two questions which I have been pondering on and I just can't figure it out. Maybe someone could be kind enough to answer the questions?

Q1; Projectile motion: Let's say we dropped a ball from a height called h.
We achieve a velocity $$v=\sqrt{2gh}$$. Let's then say that we hit the ball in differently angle with a paddle. What will the motion equations become?

Solve the system

$$m\frac{d^{2}\vec{r}}{dt^{2}}=m\vec{g}$$

with the initial conditions that u wish to impose...

Q2: Angular motion: Let's say we have a ball in vaacum. We make this ball rotate. Then this ball achieves angular velocity, the direction of the angular velocity $$\omega$$ can be found by the right-hand rule. But I am confused, what does the angular velocity's direction tell us? It it where the ball will move towards?

Thank you.

Nope.If the ball just rotates around a fix axis (for simplicity),then the direction of $\vec{\omega}$ will be along the rotation axis and,incidentally,the angular momentum $\vec{L}$ will have the same direction.So yes,i the ball doesn't translate,then specifying the modulus,sense & direction of either $\vec{L}$ or $\vec{\omega}$ will completely determine the movement,in case the ball is not acted on by any force (except gravity which would give a zero torque under normal conditions)...

Daniel.

 

[abdul]

Solve the system

$$m\frac{d^{2}\vec{r}}{dt^{2}}=m\vec{g}$$

with the initial conditions that u wish to impose...

I'm sorry to ask again. But I didn't understand your answer. How did you achieve that equation, could you show me? What is $$\vec{r}$$? Is it the radius of the ball? Let's say I impose initial conditions as none friction and none air resistance. How will the equation turn out then?

Thank you for the answer of Q2.

 

[dextercioby]

It's the II-nd law of Newton for translation movement...Mass times acceleration is equal to the vector sum of all forces acting on the body.In this case,it's only gravity.That $\vec{r}$ is the position vector for the CM of the body wrt an inertial reference system.

Daniel.

 

[abdul]

Thank you for your help, Daniel. I appreciate it.