Question

Let L be the circle in the x-y plane with center the origin and radius 38. Let S be a moveable circle with radius 8 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on S before S is rolled and the path of P is studied. The initial position of P is (38,0). The initial position of the center of S is (14,0) . After S has moved counterclockwise about the origin through an angle t the position of P is:

x = 14cost + 24cos(7/12t)
y= 14sint - 24sin (7/12t)

Required:
How far does P move before it returns to its initial position?

Answer 1

P moves = 70.73 m

Explanation:

Given data

Radius = 38

initial position of P = ( 38,0 )

initial position of center S = ( 14,0)

position of P ( after s moved counterclockwise )

: x = 14cost + 24cos(7/12t)

y = 14sint - 24sin(7/12t)

Determine how far P moves before returning to its initial position

attached below is the solution

P moves = 70.74 m