Question

8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed axis with angular speed of 10 rad/s. A constant torque of 50 Nm is applied in a direction that slows down the rotation, for 2 seconds.

(i) Calculate the angular speed of the object at t = 5 s.

(ii) Calculate the kinetic energy of the object at t = 5 s.

9.A disc of moment of inertia 10 kg m^2 about its center rotates about the center with an angular velocity of 20 rad/s. Calculate:

(i) its rotational energy

(ii) its angular momentum about the center

(iii) the number of revolutions per second of the disc

10.A constant torque of 100 N m turns a wheel which has a moment of inertia 10 kg ms^2 about its center. Find:

(i) the angular velocity gained in 2 second

(ii) the kinetic energy gained in 2 seconds.

11. Calculate the K.E. of the earth due to its rotation about its own axis. Mass of the earth is 6 x10^24 kg and radius of the earth is 6400 km.

12. The moment of inertia of a wheel is 1000 kgm^2. At a given instant, its angular velocity is 10 rad/s. After the wheel rotates through an angle of 100 radian, the wheel’s angular velocity is 100 rad/s. Calculate,

(i) the torque applied on the wheel

(ii) the increase in rotational kinetic energy

13. A disc of mass 5 kg and radius 40 cm rotates about an axis passing through its center and perpendicular to its plane. It makes 10 revolutions in one second. Calculate its ,

(i) rotational KE

(ii) angular momentum

Answer 1

Q8 -

(i)

Angular speed of the object at t=5s = 6rad/s

(ii) Kinetic Energy =

Q9 -

(i)

(ii) Angular Momentum

(iii) Number of revolutions per second =

Q10

(i)

(ii)

Q11

Earth is solid sphere, therefore its Moment of Inertia

Frequency of earth is

Q12

(i)

(ii) Increase in rotational Kinetic Energy =

Q13

(i) Moment of Inertia

(ii) Angular Momentum