Question 646: Centre of Mass and Rotational Motion

Question

A force $$\overrightarrow F  = \alpha \widehat i + 3\widehat j + 6\widehat k$$ is acting at a point $$\overrightarrow r  = 2\widehat i - 6\widehat j - 12\widehat k$$. The value of $$\alpha $$ for which angular momentum about origin is conserved is

Accepted Answer

From Newton's second law for rotational
motion,
$$\overrightarrow 	au   = {{\overrightarrow d L} \over {dt}}$$, if $$\overrightarrow L $$ = constant then $$\overrightarrow 	au   = 0$$
So, $$\overrightarrow 	au   = \overrightarrow r  	imes \overrightarrow F  = 0$$
$$\left( {2\widehat i - 6\widehat j - 12\widehat k} ight) 	imes \left( {\alpha \widehat i + 3\widehat j + 6\widehat k} ight) = 0$$
Solving we get $$\alpha $$ = Ã¢ÂÂ1

Answer

zero

Answer

1

Answer

$$-$$ 1

Answer

2

Centre of Mass and Rotational Motion

A force $\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k is acting at a point \overrightarrow r = 2\widehat i - 6\widehat j - 12\widehat k. The value of \alpha $ for which angular momentum about origin is conserved is

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