Can Circular Motion Be Calculated Like Linear Motion?

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Circular motion can be analyzed using principles similar to linear motion, but specific conditions must be met regarding the direction of force application. If the force is applied in the direction of circular motion, the arc length can be calculated using the formula d = (Ft^2)/(2m). However, angular velocity cannot simply be derived from total distance divided by radius; it requires a different approach. When the force is applied perpendicular to the ball's motion, the speed remains constant, and the distance traveled can be calculated using d = v_it + (Ft^2)/(2m). Understanding these distinctions is crucial for accurately applying linear motion equations to circular scenarios.
clm222
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.
 
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Where, and in which direction, do you apply the force?
If the force is always in direction of the circular motion (as forced by the string), that works. However, angular velocity after the acceleration is not the total distance divided by the radius. That is the angle, not its velocity.
 
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, let's 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} ?
 
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.
 

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