Advertisements
Advertisements
Question
A uniform disc of radius R, is resting on a table on its rim.The coefficient of friction between disc and table is µ (Figure). Now the disc is pulled with a force F as shown in the figure. What is the maximum value of F for which the disc rolls without slipping?
Advertisements
Solution
Let the acceleration of the centre of mass of the disc be ‘a’, then
`Ma = F - f` ......(1)
The angular acceleration of the disc is `α = a/R`. (if there is no sliding).
Then `(1/2 MR^2)α = Rf` ......(2)
⇒ `Ma = 2f`
Thus, `f = F/3`. Since there is no sliding,
⇒ `f ≤ µmg`
⇒ `F ≤ 3µMg`.
APPEARS IN
RELATED QUESTIONS
Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere.
Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^2 = (2gh)/((1+k^2"/"R^2))`.
Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5m long string. If the string makes an angle of 30° with vertical, compute its period. (g = 9.8 m/s2)
The following figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline θ is related to the acceleration a of the car as a = g tanθ. If the sphere is set in pure rolling on the incline, _____________.
A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.
Discuss rolling on an inclined plane and arrive at the expression for acceleration.
A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along with a horizontal table with a velocity of 20 cms-1. (take the surface of the table as reference)
A solid sphere of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with velocity of 10 emfs. The total kinetic energy of sphere is ______.
A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity `omega`. The tension in the strings is F. If the length of string and angular velocity are doubled, the tension in string is now ____________.
An object is rolling without slipping on a horizontal surface and its rotational kinetic energy is two-thirds of translational kinetic energy. The body is ______.
Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ______.
A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be ______.
(Force constant of the spring = 36 N/m)
The kinetic energy and angular momentum of a body rotating with constant angular velocity are E and L. What does `(2E)/L` represent?
The angular displacement of a particle in 6 sec on a circle with angular velocity `pi/3` rad/sec is ______.
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
An inclined plane makes an angle 30° with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ______. (g = acceleration due gravity) (sin 30° = 0.5)
