Question

A flywheel within large water pump is a solid disk with mass 23.5 kg and a radius of 0.36 m. Starting from rest it begins to rotate with a constant acceleration of 2.5 rad/sec2 for 5.9 sec after which it rotates at a constant rate. 1) What is the moment of interia of the flywheel? kg-m2 Submit 2) After 5.9 seconds, what is it's angular speed? rad/sec Submit 3) Though what angle has it rotated in those 5.9 seconds? rad Submit 4) How many revolutions has it completed in thoe 5.9 seconds? revolutions Submit 5) What is the magnitude of the linear velocity of a piece of metal on the very outer edge of the flywheel 4.9 seconds after it started to rotate? m/sec Submit 6) What is the magnitude of the total linear acceleration of a piece of metal on the very outer edge of the flywheel 4.9 seconds after it started to rotate? m/sec2 Submit

Answer 1

1 )

the moment of interia of the flywheel is I

I = 0.5 M r²

I = 0.5 X 23.5 X 0.36²

I = 1.522 kg.m²  

2 )

After 5.9 seconds it's angular speed is

2.5 X 5.9 = 14.75 rad/sec

3 )

the angle has it rotated in those 5.9 seconds

0.5 X 2.5 X 5.9²= 43.51 rad

4 )

the revolutions has it completed in thoe 5.9 seconds is

= 43.51 / 2 X 3.14

= 6.92 rev

5 )

the magnitude of the linear velocity of a piece of metal on the very outer edge of the flywheel 4.9 seconds after it started to rotate is

= 0.36 X 2.5 X 4.9

= 4.41 m/sec

6 )

the magnitude of the total linear acceleration of a piece of metal on the very outer edge of the flywheel 4.9 seconds after it started to rotate is

= 0.36 X 2.5

= 0.9 m/sec²