Two cylinders having radii $$2R$$ and $$R$$ and moment of inertia $$4I$$ and $$I$$ about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity $${\omega}_{0}$$. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite direction. During this
There is a finite net torque about point O, O' and A. Thus angular momentum is not conserved.
Initial K.E, $$E_i= \dfrac{1}{2} (4I) w_o^2= 2Iw_o^2$$
Final K.E, $$E_f= \dfrac{1}{2}I w_o^2 + \dfrac{1}{2} (4I) \dfrac{w_o^2}{4}= Iw_o^2$$
Thus K.E is also not conserved.
A thick walled hollow sphere has outer radius $$R$$. It rolls down an inclined plane without slipping and its speed at the bottom is $$v$$. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom will be $$5v / 4$$. What is the radius of gyration of the sphere?
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $$(K_t)$$ as well as rotational kinetic energy $$(K_r)$$ simultaneously. The ratio $$K_t : (K_t + K_r)$$ for the sphere is?
Two solid cylinders $$P$$ and $$Q$$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $$P$$ has most of its mass concentrated near its surface, while $$Q$$ has most of its mass concentrated near the axis. Which statement(s) is (are) correct ?
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
A cylinder rolls without slipping on a horizontal plane surface. If the speed of the centre is $$25\ m/s$$ what is the speed of the highest point?
A solid cylinder rolls up an inclined plane of angle of inclination 30o. At the bottom of the inclined plane the center of mass of the cylinder has a speed of 5m/s. (a) How far will the cylinder go up the plane? (b) How long will it take to return to the bottom?
A uniform solid cylinder of radius $$R=15\:cm$$ rolls over a horizontal plane passing into an inclined plane forming an angle $$\alpha=30^\circ$$ with the horizontal (figure shown above). Find the maximum value of the velocity $$v_0$$ in (m/s) which still permits the cylinder to roll onto the inclined plane section without a jump. The sliding is assumed to be absent.
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 $$20\ J$$. What are the speed of its centre of mass?
Suppose that yo-yo in Problem $$17$$, instead of rolling from rest, is thrown so that its initial speed down the string is $$1.3\ m/s$$.What is the total kinetic energy?
A small object of uniform density rolls up a curved surface with an initial velocity $$v$$. It reaches up to a maximum height of $$\dfrac{3v^2}{4g}$$ w.r.t. the initial position. The object is a: