A little boy is riding on a merry-go-round being pushed by a friend. Assume the

Question

A little boy is riding on a merry-go-round being pushed by a friend. Assume the boy is sitting 2.75 meters from the axis of rotation. The mass of the boy is 55.0 kg. The position of the boy is defined by the equation below: Find the angular position of the boy at t=4.0 seconds. Find the displacement of the boy from t=4.0 s to t= 9.0 s. Find the angular velocity of the boy at t=9.0 s. Can rotational kinematics be used in this problem? Why or why not? Find the arc distance traveled by the boy in the first 10.0 seconds of riding.

Explanation / Answer

For angular position at any time , put the value of t in the equation. Hence

A. Position will be 276rad.

B. Fodisplacement final position - initial position

3051- 276.. = 2775 rad.

C. For angular velocity, differentiate the given equation w.r.t time, 12t2 + 4t - 3. Put t = 9 here.1005rad/sec.

D. For angular acceleration differentiate equation for angular velocity, 24t + 4.

Here angular acceleration is not constant hence you can't apply kinematics.

E. For this find total angle I.e. 4170 then devide by 2 for number of cycles, I.e. 663.67 now multiply by 2R for arc length.

F. Tangential acceleration = angular acceleration × R

Hence 539 m/s2.

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