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Q.

A circular horizontal platform of radius R=1 m is rotating about a vertical axis passing through it’s centre O with an angular speed ω=1rad/s. There are two observers A and B, who are stationary wrt platform standing on it’s periphery. There is another observer C who is standing on the ground at a distance d=2 m from O. A observes a particle P to be moving with velocity V'=2m/s and acceleration a’=8 m/s2 in the direction shown. At this instant, particle P is at a distance of 2m form O. Refer the diagram of the platform from the top view. To transform the acceleration with respect to rotating observer to acceleration with respect to inertial observer, following relation can be used: a¯=a¯'+2(ω¯×V¯')+ω¯×(ω¯×r¯)+α¯×r¯  ; r¯ is instantaneous position vector of particle with respect to an origin taken on the axis of rotation, 2(ω¯×V¯') is known as axipetal acceleration,  α¯×r¯ is known as Euler’s acceleration.

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A circular horizontal platform of radius R=1 m is rotating about a vertical axis passing through it’s centre O with an angular speed ω=1rad/s. There are two observers A and B, who are stationary wrt platform standing on it’s periphery. There is another observer C who is standing on the ground at a distance d=2 m from O. A observes a particle P to be moving with velocity V'=2 m/s and acceleration a’=8 m/s2 in the direction shown. At this instant, particle P is at a distance of 2m form O. Refer the diagram of the platform from the top view. To transform the acceleration with respect to rotating observer to acceleration with respect to inertial observer, following relation can be used: a¯=a¯'+2(ω¯×V¯')+ω¯×(ω¯×r¯)+α¯×r¯  ; r¯ is instantaneous position vector of particle with respect to an origin taken on the axis of rotation, 2(ω¯×V¯') is known as axipetal acceleration,  α¯×r¯ is known as Euler’s acceleration.