When 100 J of work is done on a flywheel, its angular velocity is increased from 60 rpm to 180 rpm . What is the moment of inertia of the wheel?

Let ω 1 be the initial angular velocity and ω 2 be the final initial angular velocity. Given: N 1 = 60 rpm and N 2 = 180 rpm . ω 1 = 2 π 60 60 rad / s = 2 π rad / s ω 2 = 2 π 180 60 = 6 π rad / s Now, work done, W = K E F - K E I where K E F is the final kinetic energy and K E I is the initial kinetic energy. K E F = 1 2 I ω 2 2 , K E I = 1 2 I ω 1 2 W = 1 2 I ω 2 2 - 1 2 I ω 1 2 W = 1 2 I ω 2 2 - ω 1 2 Putting values in the formula, we get, 100 = 1 2 × I × 36 π 2 - 4 π 2 I = 200 32 π 2 I = 0 . 63 kgm 2

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Determine the kinetic energy of a circular disk rotating with a speed of $60 rpm$ about an axis passing through a point on its circumference and perpendicular to its plane. The circular disk has a mass of $5 kg$ and radius $1 m$ .

Important Questions on Systems of Particles and Rotational Motion

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11th Telangana Board

IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 12

Two particles, each of mass

m

and speed

u

, travel in opposite directions along parallel lines separated by a distance

d

. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 13

The moment of inertia of a flywheel making

300

revolutions per minute is

0.3 {kgm}^{2}

. Find the torque required to bring it to rest in

20 s

HARD

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 14

When

100 J

of work is done on a flywheel, its angular velocity is increased from

60 rpm

180 rpm

. What is the moment of inertia of the wheel?

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 7.1

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 7.2

In the HCl molecule, the separation between the nuclei of the two atoms is about

1 .27 Å

(1 Å = 10^{- 10} m)

. Find the approximate location of the CM of the molecule, given that a chlorine atom is about

35 .5

times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 7.3

A child sits stationary at one end of a long trolley moving uniformly with a speed

V

on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley

+

child) system?

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 7.4

Show that the area of the triangle contained between the vectors

a

and

b

is one half of the magnitude of

a \times b

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 7.5

Show that $a . (b \times c)$ is equal in magnitude to the volume of the parallelepiped formed on the three vectors, $a$ , $b$ and $c$ .

Determine the kinetic energy of a circular disk rotating with a speed of 60 rpm about an axis passing through a point on its circumference and perpendicular to its plane. The circular disk has a mass of 5 kg and radius 1 m.

Important Questions on Systems of Particles and Rotational Motion

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Determine the kinetic energy of a circular disk rotating with a speed of $60 rpm$ about an axis passing through a point on its circumference and perpendicular to its plane. The circular disk has a mass of $5 kg$ and radius $1 m$ .