(^632) „„„„„ A Textbook of Engineering Mechanics
and mass moment of inertia, I=Mr^2 = 395 × (1)^2 = 395 kg-m^2
We know that frictional couple (or torque T)
100 =Iα = 395 α
∴α=
(^100) 0.253 rad/s 2
395

and final angular velocity of the flywheel,
0=ω 0 – αt = 10π – 0.253 t ...(Minus sign due to retardation)
∴ t=
10
124.2 s
0.253
π
= Ans.
EXERCISE 31.1

1. A wheel has a string of length 4 m wrapped round its shaft. The string is pulled with a
   constant force of 150 N. It is observed that when the string leaves the axle, the wheel is
   rotating at 3 revolutions in a second. Find the moment of inertia of the wheel.
   [Ans. 3.38 kg-m^2 ]


2. The flywheel of a steam engine of mass 1000 kg has radius of gyration as 1 m. If the
   maximum and minimum speed of the flywheel is 80 r.p.m. and 78 r.p.m. respectively,
   find the fluctuation of energy. [Ans. 1732.7 N-m]


3. A flywheel of an engine has a mass of 1250 kg and radius of gyration 600 mm. Find the
   angular acceleration of the wheel, when it is subjected to a torque of 12 500 N-m.
   [Ans. 27.78 rad/s^2 ]


4. A constant torque of 2 kN-m is exerted on a crankshaft to start the engine. The flywheel
   has a mass of 1800 kg and radius of gyration 1 m. If there is a resisting torque of 1 kN-m,
   find the speed of the engine after 1 minute. [Ans. 320.9 r.p.m.]
   [Hint. Effective torque = 2 – 1 = 1 kN-m]


5. A flywheel of mass 400 kg and radius of gyration 1 m losses its speed from 300 r.p.m. to
   240 r.p.m. in 120 seconds. Determine the retarding torque acting on it.[Ans. 20.8 N-m]


6. A retarding torque of 600 N-m is applied to a flywheel rotating at 240 r.p.m. Find the
   moment of inertia of the flywheel, if it comes to rest in 100 seconds.[Ans. 2390 kg-m^2 ]

31.18.MOTION OF A BODY TIED TO A STRING AND PASSING OVER A

PULLEY

Consider a body tied to a string and passing over a pulley as

shown in Fig. 31.8. Let the body descend under the force of gravity.

Let m= Mass of the body

M= Mass of the pulley

I= Moment of inertia of the pulley,

r= Radius of the pulley,

k= Radius of gyration of the pulley.

a= Linear acceleration of the body,

α= Angular acceleration of the pulley,

and

P= Pull in the string Fig. 31.8. Motion of one body.