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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Four particles each of mass $100 g$ are placed at the corners of a square of side $10 cm$ . Find the moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane. Find also the radius of gyration of the system.

Important Questions on Systems of Particles and Rotational Motion

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

Two uniform circular discs, each of mass

1 kg

and radius

20 cm

, are kept in contact. Find the moment of inertia of the system of two discs about the tangent passing through their point of contact.

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Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 8

Four spheres each diameter

2 a

and mass

' m'

are placed with their centres on the four corners of a square of the side

b

. Calculate the moment of inertia of the system about any side of the square.

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Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 9

To maintain a rotor at a uniform angular speed of

200 rad s^{- 1}

, an engine needs to transmit a torque of

180 Nm

. What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is

100 %

efficient.

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Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 10

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass

5 g

are put on top of the other at the

12.0 cm

mark, the stick is found to be balanced at

45.0 cm

. What is the mass of the metre stick?

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Intermediate First Year Physics>Chapter 7 - Systems of Particles and Rotational Motion>EXERCISES>Q 11

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

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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

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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?

Four particles each of mass 100 g are placed at the corners of a square of side 10 cm. Find the moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane. Find also the radius of gyration of the system.

Important Questions on Systems of Particles and Rotational Motion

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Four particles each of mass $100 g$ are placed at the corners of a square of side $10 cm$ . Find the moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane. Find also the radius of gyration of the system.