# Rotational Kinematics

## Homework Statement

This isn't so much of a problem as a general question. I am trying to find the starting velocity of a spinning ball going upwards (in air, close to earth's surface, only force acting on it is the gravitational force) until its linear velocity reaches zero. I found the initial velocity two different ways (with mechanical energy and with kinematics), and I am getting answers that differ by a constant.

## Homework Equations

$mgh=\frac{7}{10}mv_0^2$

$v_f^2=v_0^2-2gh$
(where the final velocity is 0)

## The Attempt at a Solution

When I try to find the initial velocity, I can see that the two differ by a constant. I know that if the ball had no rotational kinetic energy, the equations would line up. However, I thought that the rotational motion would not have an effect on the linear motion of its center of mass. I think that the discrepancy is because the kinematics equation is derived from the conservation of energy of an object that has no rotational motion, but I'm not sure. I appreciate your help!

Yes. If you set $mgh$ = $\frac{1}{2}$mv2 then you get that the initial velocity is $\sqrt{2gh}$. This is the same as the result from the kinematics equation when the final velocity is zero.