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physics

mechanics

Easy

Question

$text A projectile of mass end text straight m text is launched with an initial velocity end text v with not stretchy rightwards arrow on top subscript i text making an angle end text theta text with the end text text horizontal as shown in figure. The projectile moves in the gravitational field of the Earth. The end text text angular momentum of the projectile about the origin when it is at the highest point of its end text text trajectory is end text$

$\frac{- m v_{i}^{3} \sin θ^{2} \cos θ}{2 g} \hat{k}$
$\frac{m v_{i}^{3} / \sin θ^{2} \cos θ}{2 g} \hat{k}$
$\frac{- m v_{i}^{3} \sin θ^{2} \cos θ}{g} \hat{k}$
$\frac{2 m v_{i}^{3} \sin θ^{2} \cos θ}{g} \hat{k}$

The correct answer is: $\frac{- m v_{i}^{3} \sin θ^{2} \cos θ}{2 g} \hat{k}$

$x equals 1 half R equals fraction numerator v subscript i superscript 2 sin invisible function application 2 theta over denominator 2 g end fraction text and end text y equals h subscript max equals fraction numerator open parentheses v subscript i sin invisible function application theta close parentheses squared over denominator 2 g end fraction L with not stretchy rightwards arrow on top subscript 1 equals r with not stretchy rightwards arrow on top subscript 1 cross times m v with not stretchy rightwards arrow on top subscript 1 equals open square brackets fraction numerator v subscript i superscript 2 sin invisible function application 2 theta over denominator 2 g end fraction i with not stretchy hat on top plus fraction numerator open parentheses v subscript i sin invisible function application theta close parentheses squared over denominator 2 g end fraction j with not stretchy hat on top close square brackets cross times m v subscript x i end subscript i with not stretchy hat on top equals fraction numerator negative m v subscript i superscript 2 sin invisible function application theta squared cos invisible function application theta over denominator 2 g end fraction k with not stretchy hat on top$

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$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

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Consider an isolated system moving through empty space. The system consists of objects that interact with each other and can change location with respect to one another. Which of the following quantities can change in time?

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PhysicsMechanics

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