A cylindrical merry-go-round can rotate freely about its central vertical axis
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A cylindrical merry-go-round can rotate freely about its central vertical axis. During a 12-s interval its angular momentum L (in kg·m²/s) is observed to vary linearly between the values listed below.
t (s)
0
3
5
9
12
L (kg·m²/s)
−10
−4
6
6
−2
Between the tabulated points, L varies linearly.
(a) For each of the four time intervals defined by successive data points, derive an algebraic expression for the net external torque as a function of time.
(b) Using the expressions from part (a), construct a scaled graph of torque versus time covering 0 ≤ t ≤ 12 s. Clearly label numerical values on both axes.
(c) Calculate the total angular impulse delivered to the merry-go-round during the 12-s interval.
(d) A student argues that the largest-magnitude torque must have occurred between t = 5 s and t = 9 s because the angular momentum there has the greatest absolute value. Evaluate this claim quantitatively using your earlier results.