Rotational Dynamics
A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is
A holosphere of radius $$0.15\ m$$, with rotational inertia $$I=0.040\ kg. m^2$$ about a line through its centre of mass, rolls without slipping up a surface inclined at $$30^o$$ to the horizontal. At a certain initial position, the sphere's total kinetic energy is $$20\ J$$. How much of this initial kinetic energy is rotational?
A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is
A uniform rod of length $$2a$$ is held with one end resting on a smooth horizontal table making an angle $$\alpha$$ with the vertical. When the rod is released
In figure, a solid ball rolls smoothly from rest (starting at height $$H=6.0\ m$$) until it leaves the horizontal section at the end of the track, at height $$h=2.0\ m$$. How far horizontally from point $$A$$ does the ball hit the floor?
In figure, a constant horizontal force $$\vec F_{app}$$ of magnitude of $$10\ N$$ is applied to a wheel of mass $$10\ kg$$ and radius $$0.30\ m$$. The wheel rolls smoothly on the horizontal surface, and the acceleration of its centre of mass has magnitude $$0.60\ m/s^2$$. In unit-vector notation, what is the frictional force on the wheel?
A bowler throws a bowling a lane. The ball slides on the lane with initial speed $$v_{com.0}=8.5\ m/s$$ and initial angular speed $$\omega _0 =0$$. The coefficient of kinetic friction between the ball and the lane is $$0.21$$. The kinetic friction force $$\vec f_{k}$$ acting on the ball causes an angular acceleration of the ball. When speed $$v_{com}$$ has decreases enough and angular speed $$\omega$$ has increased enough, the ball stops sliding and then rolls smoothly. How long does the ball slide?
A ring, cylinder and solid sphere are placed on the top of a rough incline on which the sphere can just roll without slipping. When all of them are released at the same instant from the same position, then :
A semi-circular track of radius $$R=62.5cm$$ is cut in a block. Mass of block, having track, is $$M=1kg$$ and rests over a smooth horizontal floor. A cylinder of radius $$r=10cm$$ and mass $$m=0.5kg$$ is hanging by a thread such that axes of cylinder and track are in same level and surface of cylinder is in contact with the track as shown in figure. When the thread is burnt, cylinder starts to move down the track. Sufficient friction exists between surface of cylinder and track, so that cylinder does not slip. Calculate velocity of axis of cylinder (in m/s) when it reaches bottom of the track. ($$g=10{ms}^{-2}$$).