A body in uniform circular motion goes through a circle of radius 3 m with a constant tangential velocity of 27 m/s. What is the centripetal acceleration of the mobile? What is the distance traveled after 6.3 seconds (in meters)?
Solution with FisicaLab
Select the Kinematic group and, inside this, the Particles circular module. Erase the content of the chalkboard and select the SI system. Now add one element Mobile with circular motion, one element Arc length and one element Stationary reference system. As show the image below:
To the element Stationary reference system we have:
The element Mobile with circular motion gonna be called Mobile. And we assume that the initial position correspond to the angle 0. Also, we left the center like 0 (to this problem the center of rotation is irrelevant). And the final velocity is left as unknown data, because the element have an entry to tangential acceleration and this assume that the final velocity is different from the initial. Also the centripetal acceleration at initial and end time are unknown data:
In the element Arc length we set our Mobile, and the arc length value is of course an unknown data:
Now click in the icon Solve to get the answer:
aci = 243.000 m/s2 ; angf = 8.671 degrees ; vf = 27.000 m/s ; acf = 243.000 m/s2 ; s = 170.100 m ; Status = success.