Motion of Projection of A Body Moving in Circle

• If a body is moving in circle then its projection is the shadow formed on the diameter of circle
• If body is moving in circle, then its velocity is always tangent to the circle and makes angle 90⁰ with radius
• If body is moving in circle, acceleration produced in it is centripetal acceleration which is always directed towards the center of circle
• If projection is formed on x-axis, then its velocity is the x-component of the velocity of body moving in circle
• If projection is formed on y-axis, then its velocity is the y-component of the velocity of body moving in circle
• The acceleration of projection is directed towards mean position, so the motion of projection is simple harmonic motion

Instantaneous displacement:

$$x=x_{0}\cos\omega t$$

Instantaneous velocity:

$$v= \omega \sqrt{x^2_{0}-x^2}$$

Instantaneous acceleration:

$$a_{x}=\omega^2 (-x)$$