# A ball hitting a person above his center of mass

We have inelastic impacts between a ball and a person. The ball is moving and the human is in rest. It hits him first in his Center of mass. In this part question it is imagined that the human stands on ice and he (gets pushed without friction .. yea i know but as i said idealize!) such that we can imply the conversation of momentum.

the part which confused me is this

What happens when the ball hits ABOVE the Center of mass?

So i thought well, maybe the ball will cause a Torque on the horizontal axis of rotation of this human since it is changing its Momentum and we know that the change of momentum / time = force and the distance $$d$$ where teh ball hits from the Center of mass will give us our Torque $$d * F$$

• This old post is about what happens when a force is applied below the center of mass. physics.stackexchange.com/q/95234/37364 May 1, 2020 at 22:37
• May 2, 2020 at 0:34

What is the definition of momentum?

Momentum is mass times the velocity of the center of mass.

So Newton's second law says a force or impulse will change the momentum regardless of where this force/impulse is applied.

\begin{aligned} p & = m \,v_{\rm COM} & & & \text{(momentum) }p \\ J & = \Delta p = m \, \Delta v_{\rm COM} & & & \text{(impulse) }J\\ F & = \frac{\rm d}{{\rm d}t} p = m \frac{\rm d}{{\rm d}t} v_{\rm COM} & & & \text{(force) }F \end{aligned}

That is all you need to know to describe the motion of the center of mass.

Now for the motion about the center of mass, you need to consider the torque applied about the center of mass. Here is the concept of angular momentum and mass moment of inertia is introduced.

\begin{aligned} L_{\rm COM} & = I_{\rm COM} \,\omega & & & \text{(angular momentum) }L \\ r \times J & = \Delta L_{\rm COM} = I_{\rm COM} \, \Delta \omega & & & \text{(impulse position) }r\\ \tau_{\rm COM} & = \frac{\rm d}{{\rm d}t} L_{\rm COM} & & & \text{(torque) }\tau \end{aligned}

If you know the mass moment of inertia $$I_{\rm COM}$$ is the human about the center of mass, you can calculate the effect of an offset impulse $$J$$ to the change in rotational speed $$\Delta \omega$$ with the second equation above.

• So answering the question according to you is as follows: 1) The ball will change the linear momentum of the human nevertheless since it is applying a force. And follows from the Newtonian law that the object will change movement. 2) The ball shall cause rotational torque around the Center of mass causing the human to rotate (Either fully or partly) Right?