A particle is securely placed on a uniformly rotating turntable. When observed from the ground, the particle travels in a circle with a speed of 20 cm/s and an acceleration of 20 cm/s ^2 . The particle is subsequently relocated to a new position, making the radius half of its initial value. Determine the new values for the speed and acceleration.

Step-by-step solution

For a particle on a uniformly rotating turntable, the angular velocity remains constant. The initial speed is given by v₁ = r₁ = 20 cm/s . The initial centripetal acceleration is given by a₁ = ^2 r₁ = 20 cm/s ^2 . When the particle is relocated such that the new radius is r₂ = r₁ 2 , the new speed v₂ is: v₂ = r₂ = ( r₁ 2 ) = v₁ 2 = 20 2 = 10 cm/s The new acceleration a₂ is: a₂ = ^2 r₂ = ^2 ( r₁ 2 ) = a₁ 2 = 20 2 = 10 cm/s ^2