Question

Question #30361

Answer 1

`"please see animation and explanation section."`

Explanation:

`"Let assume that P is an object revolving around 'O' with a"`
`"radius of r. v shows the velocity vector of P. Direction of the "` `"velocity is change but its magnitude does not change.The "` `"object revolves the same angle in every unit time. To the "` `"motion which is shown the animation above we say 'uniform "` `"circular motion'."`

`"Please notice to these points."`

• the velocity vector v is tangent to the circle.
• A force pointing pivot point occurs(the centripetal force).
• The centripetal force is perpendicular to the tangential velocity.
• The time for a full revolution is the period(T).
• The tangential velocity can be calculated using the formula
  `v=(2pi r)/T`
• the angular velocity of object can be calculated using the formula
  `omega=(2 pi)/T`
• the unit of the angular velocity is rad/sec
• using the two equation above ,we obtain the equation v=w.r
• The angular acceleration of object is pointed to the pivot point.
• The angular acceleration is calculated using:
  `a=v^2/r" or "a=omega^2.r`
• You can calculate the centripetal force using Newton's second law.

`F=m.a" , "F=(m v^2)/r" , "F=m omega^2 r`