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. - Physics


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.



Total Rolling kinetic energy = Translational K. E. + Rotational K. E.

`=1/2 MV^2+1/2 Iomega^2`


`omega=V/R `

`"Total Rolling K.E" = 1/2 MV^2+1/2 I(V^2/R^2)`

`"for solid sphere" I=2/5 MR^2`

`"Total Rolling K.E."=1/2 MV^2+1/2 (2MR^2)/5(V^2/R^2)`

`=1/2 MV^2+1/5 MV^2`

`=7/10 MV^2`

Concept: Rolling Motion
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2012-2013 (March)



Read each statement below carefully, and state, with reasons, if it is true or false;

The instantaneous speed of the point of contact during rolling is zero.

Read each statement below carefully, and state, with reasons, if it is true or false;

A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion

A solid sphere of mass 1 kg rolls on a table with linear speed 2 m/s, find its total kinetic energy.

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‘θ’ then linear acceleration of body rolling down the plane is _______.

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Can an object be in pure translation as well as in pure rotation?

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A hollow sphere and a solid sphere having same mss and same radii are rolled down a rough inclined plane.

A sphere cannot roll on

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(a) on the rear wheels is in the forward direction

(b) on the front wheels is in the backward direction

(c) on the rear wheels has larger magnitude than the friction on the front wheels

(d) on the car is in the backward direction.

A sphere can roll on a surface inclined at an angle θ if the friction coefficient is more than \[\frac{2}{7}g \tan\theta.\] Suppose the friction coefficient is \[\frac{1}{7}g\ tan\theta.\] If a sphere is released from rest on the incline, _____________ .

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, _____________.

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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.

A hollow sphere is released from the top of an inclined plane of inclination θ. (a) What should be the minimum coefficient of friction between the sphere and the plane to prevent sliding? (b) Find the kinetic energy of the ball as it moves down a length l on the incline if the friction coefficient is half the value calculated in part (a).

Discuss the interlink between translational, rotational and total kinetic energies of a rigid object rolls without slipping.

Answer in Brief:

A rigid object is rolling down an inclined plane derive the expression for the acceleration along the track and the speed after falling through a certain vertical distance.

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The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, ______

What is the condition for pure rolling?

What is the difference between sliding and slipping?

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)

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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?

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(Force constant of the spring = 36 N/m)

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