Question

A 3.1-m-diameter merry-go-round with rotational inertia 110 kg · mº is spinning freely at 0.60 rev/s . Four 25-kg children sit suddenly on the edge of the merry-go-round. Find the new angular speed. Express your answer using two significant figures. IVO AQ R O 2 ? 1 rev/s Submit Request Answer Part B Determine the total energy lost to friction between the children and the merry-go-round. Express your answer using two significant figures. IVO AQ R O 2 ? AK =

Answer 1

Solution) d = 3.1 m

Radius , r = (d/2) = (3.1/2) = 1.55 m

I1 = 110 kgm^2

w1 = 0.60 rev/s

m = 25 kg

M = 4m = 4×25 = 100 kg ( total mass of 4 children)

(A) New angular speed , V = ?

I2 = I1 + M(r^2)

I2 = 110 + 100(1.55^2)

I2 = 350.25 kgm^2

Applying conservation of angular momentum

(I1)(w1) = (I2)(w2)

(110)(0.60) = (350.25)(w2)

w2 = (110×0.60)/(350.25)

w2 = 0.188 rev/s

(B) delta K = ?

delta K = KEi - KEf

delta K = (1/2)(I1)(w1^2) - (1/2)(I2)(w2^2)

delta K = (1/2)(110)(0.60×2(pi))^2 - (1/2)(350.25) (0.188×2(pi))^2

delta K = 781 - 243.42 = 537.58 J

delta K = 5.37×10^(2) J

delta K = 5.4×10^(2) J