The radius of a park merry-go-round is 1.7 m. To start it rotating, you wrap a r

Question

The radius of a park merry-go-round is 1.7 m. To start it rotating, you wrap a rope around it and pull with a force of 260 N for 19 s. During this time, the merry-go-round makes one complete rotation.

(a) Find the angular acceleration of the merry-go-round. Incorrect: Your answer is incorrect. rad/s2

(b) What is the magnitude of the torque exerted by the rope on the merry-go-round? Incorrect: Your answer is incorrect. N·m

(c) What is the moment of inertia of the merry-go-round? Incorrect: Your answer is incorrect. kg·m2

Explanation / Answer

radius r=1.7 m

force F=260 N

tme t=19 sec

for one complete roatation,

angular displacement, theta=2pi rad

w=2pi*1.7/19

w=0.56 rad/sec

a)

let,

angular acceleration is alpa

theta=1/2*alpa*t^2

2pi=1/2*alpa*19^2

alpa=0.035 rad/sec^2

b)

torque =r*F

=1.7*260

= 442 N.m

c)

let

moment of inertia is I

then,

torque =I*alpa

442=I*(0.035)^2

===> I=3.61*10^5 kg.m^2

moment of inertia I=3.61*10^5 kg.m^2

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