Q: Incorrectly pursue a tangential legal issue

A: Tangential Velocity in Uniform Circular Motion
We have a cute little experiment which exercises some of the equations we have discussed in this lecture. We have a mechanism by which I can make a ball perform uniform circular motion. [ [ Again for now it is not crucial how this is achieved but I can say that the string is instrumental in giving rise to the required centripetal acceleration.

With a razor blade I can cut the string at which point the ball performs projectile motion with an initial velocity which matches the instantaneous velocity vector at the time the string was cut.
Performing the experiment you clearly see that without the string to induce the centripetal acceleration the ball is ejected in the tangential direction. On the table we have a carbon paper which enables us to see where the ball first hits the table. From how far it goes I can determine the magnitude of the initial velocity and I will compare that number with the number I can derive from known parameters of the uniform circular motion.
We first write an expression for the trajectory of the particle as it is released from its circular orbit. We use Eq. gif with tex2html_wrap_inline172 (the ball comes out horizontal)
equation29
To determine tex2html_wrap_inline174 we use our knowledge that the point of impact lies on the trajectory. We measure that relative to the point of release the point of impact is given by
equation34
We insert tex2html_wrap_inline176 in Eq. 8 and solve for tex2html_wrap_inline174 to get
eqnarray37
The other way to calculate tex2html_wrap_inline174 is to use the known parameters of the circular motion. We have R=0.40 m and T=0.52 s which implies that
eqnarray43
The two calculations agree well indicating that we do understand something about projectile motion and uniform circular motion. ] ]

Galbatoryx|Points 46|

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