How much fraction of the kinetic energy of rolling is purely:
- Translational.
- Rotational.
Download our app for free and get started
- Fraction of translational kinetic energy
$=\frac{\text{r}^2}{(\text{k}^2+\text{r}^2)}$
- Fraction of rotational kinetic energy
$=\frac{\text{r}^2}{(\text{r}^2+\text{k}^2)}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass: Show $\frac{\text{dL}}{\text{dt}}=\sum\text{r}'_\text{i}\times\frac{\text{dp}'}{\text{dt}}$ Further, show that $\frac{\text{dL}'}{\text{dt}}=\tau'_\text{ext}$ where $\tau'_\text{ext}$ is the sum of all external torques acting on the system about the centre of mass.View Solution
(Hint: Use the definition of centre of mass and third law of motion. Assume the internal forces between any two particles act along the line joining the particles) - 2$(n - 1)$ equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.View Solution
- 3View SolutionEstablish the relationship between Torque and Moment of Inertia.
- 4View SolutionA metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on top of the other at the 12.0cm mark, the stick is found to be balanced at 45.0cm. What is the mass of the metre stick?
- 5View SolutionFind the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.
- 6A non-uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in. The angles made by the strings with the vertical are $36.9°$ and $53.1°$ respectively. The bar is $2m$ long. Calculate the distance d of the centre of gravity of the bar from its left end.View Solution
- 7View SolutionA disc of radius R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.
- 8View SolutionShow that a(b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors a, b and c.
- 9View SolutionCalculate the total torque acting on the body shown in figure about the point O.
- 10Figure shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R.View Solution
- Find the kinetic energy of the ball when it is at a point A where the radius makes an angle $\theta$ with the horizontal.
- Find the radial and the tangential accelerations of the centre when the ball is at A.
- Find the normal force and the frictional force acting on the ball if H = 60cm, R = 10cm, $\theta=0 $ and m = 70g.
