A playground merry-go-round has a radius of 4.60 m and a moment of inertia of 24

Question

A playground merry-go-round has a radius of 4.60 m and a moment of inertia of 240 kg*m^2 and turns with negligible friction about a vertical axle through its center.

A)A child applies a 20.0 N force tangentially to the edge of the merry-go-round for 18.0 s . If the merry-go-round is initially at rest, what is its angular velocity after this 18.0 s interval?

w = _____ rad/s

B)How much work did the child do on the merry-go-round?

W = _____ J

C)What is the average power supplied by the child?

P = ____ W

Explanation / Answer

A playground merry go around has a radius of 4.60 m and a moment of inertia of 240 kg * m^2 and turns with negligible friction about a vertical axle through its center.

A child applies a 25.0 N force tangentially to the edge of the merry go around for 20s. If the merry go around is initially at rest, what is its angular velocity after this 20s interval?

w = rad/s

How much work did the child do on the merry go around?

W = J

What is the average power supplied by the child?

P= W

(1) Using T = I (/t)
T = torque = (25N x 4.6m) Nm
I = mom. of inertia
/t = angular acceleration (rad/s²)

/t = (25N x 4.6m) / (240) = 0.479 rad/s²
so = 0.479 rad/s² x 20 s ... ........... ........= 9.6 rad/s

(2) Work done = KE gained = ½ I ²
W = ½(240)(9.6)² .. .. ....................... ........... = 11,059 J

(3) Power = W/t .. (J/s)
P = 11059 / 20 s .. ... .. ....... .............. ........ = 553 W

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