Question

A person of mass 80 kg stands at the center of a rotating merry-go-round platform of radius 3.5 m and moment of inertia 950 kg*m^2 . The platform rotates without friction with angular velocity 0.85 rad/s . The person walks radially to the edge of the platform.

1.Calculate the angular velocity when the person reaches the edge.
w=______________ rad/s

2.Calculate the rotational kinetic energy of the system of platform plus person before the person's walk.
Ki=____________ J

3.Calculate the rotational kinetic energy of the system of platform plus person after the person's walk.
Kf=__________ J

Answer 1

Given that

Mass of person, m = 80 kg

radius of merry, r = 3.5 m

   I1 = 950 kg.m^2

   I2 = I1 + mr^2 = 950 + 80 * 3.5^2 = 1930 kg.m^2

    ω1 = 0.85 rad/s

1.

According to conservation of angular momentum we have

   I1*ω1 = I2 *ω2

From the above above we have

    ω2 = 950 * 0.85 / 1930 = 0.42 rad/s

2.

The initial rotational kinetic energy is given by the formula

J = (1/2)I1*ω1^2

     = 0.5 * 950 * (0.85)^2 = 343.18 J

3.

The fianl rotational kinetic energy is given by the formula

   J = (1/2)I2*ω2^2

     = 0.5 * 1930 * 0.42^2 = 170.23 J

Answer 2

Answer question