Chapter 12 - Rotation of a Rigid Body - Exercises and Problems - Page 350: 44

The magnitude of the angular momentum relative to the origin is $1.3~kg~m^2/s$ in the clockwise direction.

Work Step by Step

We can find the momentum vector of the particle as: $p = (m~v_x)~\hat{i}+(m~v_y)~\hat{j}$ $p = (0.20~kg)(3.0~m/s)~cos(45^{\circ})~\hat{i}- (0.20~kg)(3.0~m/s)~sin(45^{\circ})~\hat{j}$ $p = (0.424~\hat{i})~kg~m/s-(0.424~\hat{j})~kg~m/s$ We can express the particle's position as a vector; $r = (1.0~\hat{i})~m+(2.0~\hat{j})~m$ We can find the angular momentum relative to the origin. $L = r\times p$ $L = [(1.0~\hat{i})~m+(2.0~\hat{j})~m]\times [(0.424~\hat{i})~kg~m/s-(0.424~\hat{j})~kg~m/s]$ $L = -(0.424~\hat{k})~kg~m^2/s-(0.848~\hat{k})~kg~m^2/s]$ $L = -(1.3~kg~m^2/s)~\hat{k}$ The magnitude of the angular momentum relative to the origin is $1.3~kg~m^2/s$ in the clockwise direction.

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