Paragraph: A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity is an example of a non-inertial frame of reference. The relationship between the force F _ rot experienced by a particle of mass m moving on the rotating disc and the for

Step-by-step solution

Force on block along slot = m ω 2 r = m a = m v d v d r ∫ 0 v v d v = ∫ R 2 r ω 2 r d r v 2 2 = ω 2 2 r 2 - R 2 4     ⇒       v = ω r 2 - R 2 4 = d r d t ⇒       ∫ R 4 r d r r 2 - R 2 4 = ∫ 0 t ω d t l n   r + r 2 - R 2 4 R 2 - l n   R 2 + R 2 4 - R 2 4 R 2 = ω t ⇒       r + r 2 - R 2 4 = R 2 e ^ ω t ⇒       r 2 - R 2 4 = R 2 4   e 2 ω t + r 2 -