# Velocity w/axis vs without

by clm222
Tags: velocity, w or axis
 P: 35 Hi, quick question I've just started to learn circular motion and i tried a basic force problem. Imagine there is a ball on a string with a string length 'r', and a ball mass 'm'. You apply a force 'F' for one second. Can the arc length of the ball's motion be calculated the same as linear motion? $d=\frac{F{t^2}}{2m}$ (replacing acceleration with F/m, vi=0) Can I also go as far as the find the angular velocity by dividing by the radius? $$ω=\frac{F{t^2}}{2mr}$$ Thanks.
 P: 35 oh ok, so if i were to have the force constantly be applied perpendicular to the ball than i CAN use the distance formula? if so, lets say the ball has initial velocity 'vi', and a force is applied, the final velocity can be calculated using ${v_f}={v_i}+\frac{Ft}{m}$, could i also calculate the distance travled: $d={v_i}t+\frac{F{t^2}}{2m}$ ?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,552 Velocity w/axis vs without If the force is applied perpendicular to the motion of the ball then its speed is constant. The distance around the circle in time t is $v_it$.