A unit mass at position vector $\vec { r } = ( 3 \hat { i } + 4 \hat { j } )$ is moving with a velocity $\vec { v } = ( 5 \hat { i } - 6 \hat { j } )$ What is the angular momentum of the body about the origin
A man standing on a platform holds weights in his outstretched arms. The system rotates freely about a central vertical axis. If he now draws the weights inwards close to his body,
A particle performs uniform circular motion with an angular momentum L. If the frequency of particle's motion is doubled and its kinetic energy halved, the angular momentum becomes:
What is the magnitude of vertical force required to produced a moment of 20 Nm at point A (1 m, 1 m) if the force is acting at point B (2m,2m)
A stone tied to one end of the string is revolved round a rod in such a way that the string winds over the rod and get shortened. In this process which of the following quantities remain constant?
A swimmer while jumping into water from a height easily forms a loop in air, if
If no external force acts on a system
Two loops P and Q are made from a uniform wire. The radii of P and Q are $r _1$ and $r _2$ respectively, and their moments of inertia about their own axises are $I _1$ and $I _2$ respectively. If $I _2 = 4I _1$, the $r _1/r _2$ equals:
A particle moves on a circular path with decreasing speed. Choose the correct statement.
A particle of mass 2 kg located at the position $ \left( \hat { i } +\hat { j } \right) m $ has a velocity $ 2\left( \hat { i } -\hat { j } +\hat{ k } \right) ms^{-1} $ . Its angular momentum along z-axis in $ kgm^2 s^{-1} $ is