About Rotational Inertia

What Rotational Inertia is and How it Affects Your Everyday Life

Have you ever wondered why it's harder to get moving on a cold day than on a warm one? It has to do with rotational inertia- the tendency of an object to resist changes in its rotational motion. The rotational inertia of an object depends on its mass and shape. A more massive object has more rotational inertia, and a more compact object has less.

On a cold day, your muscles are stiffer and have less rotational inertia than they do on a warm day. That's why it's harder to get moving. But once you're moving, it's easier to keep going. That's because rotational inertia also depends on the rotational speed of an object.

So, when you're trying to get moving on a cold day, you have to overcome both the stiffness of your muscles and their low rotational inertia. But once you're moving, your muscles have more rotational inertia and can keep you going.

Wrapping Up

That's rotational inertia in a nutshell. It's a simple concept, but it has a big impact on your everyday life. The next time you're struggling to get out of bed on a cold morning, remember rotational inertia and give yourself a little extra push.

Following are some of the multiple choice questions on the Rotational Inertia with answers that will help the students in developing their knowledge.

Rotational Inertia MCQ

1. What is the angular speed about the rotational axis of the Earth for a person standing on the surface?

  • 7.3 x 10-5 rad/s
  • 3.6 x 10-5 rad/s
  • 6.28 x 10-5 rad/s
  • 3.14 x 10-5 rad/s

2. Which is the wrong relation from the following?

  • τ = I α
  • F = ma
  • L = I ω
  • I = τ α

3. The easiest way to open a heavy door is by applying the force

  • Near the hinges
  • In the middle of the door
  • At the edge of the door far from the hinges
  • At the top of the door

4. The unit of angular velocity is

  • m/s
  • m/s²
  • rad/s
  • rad/s²

5. Molecules which are having _______ are microwave active.

  • Dipole moment
  • High pressure Detector
  • Principle axis
  • Acidity

6. 2600 rev/min is equivalent to which of the following?

  • 2600 rad/s 
  • 43.3 rad/s 
  • 273 rad/s
  • 60 rad/s

7. Suppose you are designing an engineless car for a downhill coasting race. What type of wheels would be the best?

  • Solid disks.
  • Hoops.
  • Hollow cylinders.
  • Diamond encrusted triangles.

8. Three homogeneous ridged bodies -- a solid shere, a solid cylinder, and a hollow cylinder -- are placed at the top of an incline. If all are released from rest at the same elevation and rolls without slipping, which reaches the bottom first?

  • The solid sphere.
  • The solid cylinder.
  • The hollow cylinder.
  • They will all arrive at the same time.

9. A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

  • the moment of inertia of the system increases and the angular speed increases.
  • the moment of inertia of the system decreases and the angular speed remains the same.
  • the moment of inertia of the system decreases and the angular speed decreases.
  • the moment of inertia of the system decreases and the angular speed increases.

10. A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy?

  • 0.092 J
  • 17 J
  • 1.1 J
  • 0.18 J

11. The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel?

  • 10.4 rad/s2
  • 3.43 rad/s2
  • 5.20 rad/s2
  • 1.06 rad/s2

12. Is torque independent of the location of the origin?

  • Yes, always.
  • Yes, as long as the origin is either in the center or on one end.
  • No, you always need to specify the origin.
  • All of above

13. The rotational inertia of an object is greater when most of the mass is located

  • away from the axis (center)
  • near the center
  • on the rotational axis ( center)
  • None of these

14. Which object listed below has the greatest momentum?

  • A 0.05 kg object rolling at 0.2 m/s.
  • A 0.15 kg object rolling at 2 m/s.
  • A 0.15 kg object rolling at 1 m/s
  • A 0.4 kg object rolling at 2 m/s.

15. What would happen to the length of one day if Earth's moment of inertia were to increase?

  • The day would be longer.
  • The day would be shorter.
  • The day would stay the same.
  • All of above

16. What is Newton's 3rd Law?

  • For every action there is an equal and opposite reaction.
  • Acceleration depends on two variables, the mass of the object and the amount of force.

17. A push or a pull is called a

  • Gravity
  • Force

18. Which would have the LEAST gravitational potential energy (GPE)?

  • A ball sitting on the ground
  • Moon viewed from the Earth
  • An airplane flying 30,000 feet above the ground
  • A rock sitting on top of Mt. Everest

19. A bowling ball has a mass of 7.00 kg, a moment of inertia of 0.056 kg·m2, and a radius of 0.100 m. If it rolls down the lane without slipping at an angular speed of 4.00 rad/s, what is its rotational kinetic energy?

  • 0.280 J
  • 0.448 J
  • 0.896 J
  • 11.2 J

20. Which equation defines rotational kinetic energy?

  • K=1/2mw2
  • k=1/2Iw2
  • k=1/2Iv2
  • k=1/2mv2

21. A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground?

  • 66 N
  • 740 N
  • 23 N
  • 44 N

22. What is the angular acceleration of an object that has rotational inertia of 4 kg.m2 and submitted to a torque of 8 N.m?

  • 0.5 rad/s2
  • 2 rad/s2
  • 4 rad/s2
  • 8 rad/s2

23. The object with more rotational inertia needs more torque to move than object with lower inertia?

  • True
  • False

24. If the same torque is applied on a hoop (I=MR2) and a solid disk (I=1/2MR2), after 5s which object will be moving faster?

  • Hoop
  • Solid Disk

25. The value of torque depends on the rotation axis and the _______________________

  • magnitude of applied force.
  • mass of object
  • moment inertia of object
  • shape of object

26. Torque can be positive or negative.

  • True
  • False

27. From the rotational microwave spectrum of 1H35Cl, we find that B = 10.59342 cm-1 . Given that the masses of 1H and 35 Cl are 1.0078250 and 34.9688527 amu, respectively, determine the bond length of the 1H35Cl molecule

  • 1.274 x 10-10 m
  • 1.674 x 10-10 m
  • 1.474 x 10-10 m
  • 1.0274 x 10-10 m

28. __________ (ω)– the rate at which a body rotates about an axis (radians per second)

  • linear speed
  • rotational speed
  • angular speed
  • velocity

29. The microwave active molecules are

  • HCl, OCS
  • CO,CO2
  • Both a) and b)
  • None of the above

30. Conditions for equilibrium are:1st condition: net force = 02nd condition:net torque = 0

  • True
  • False

31. Calculate the moment of inertia, I, of the molecule 1H35Cl. The masses of the two atoms are mH = 1.673 x 1027 kg and mCl = 5.807 x 1026 kg. The equilibrium bond length of the molecule is 1.275 Å.

  • 2.644 x 1047 kg m2
  • 2.644 x 1027 kg m2
  • 2.644 x 1044 kg m2
  • 2.644 x 1024 kg m2

32. Which of the following molecule has no rotational spectrum?

  • NH3
  • HCl
  • N2
  • H2O.

33. The photon described in Question 3 lies within which part of the electromagnetic spectrum?

  • Radio wave
  • Visible
  • Infrared
  • Ultraviolet

34. The energy in joules of a photon of wavelength 355 nm is

  • 5.596 x 1019 J
  • 5.596 x 1028 J

35. A photon of wave number 100 cm-1 has a wavelength of

  • 1 m
  • 1 mm
  • 1000 nm
  • 100 m

36. The different types of energies associated with a molecule are __________

  • Vibrational energy
  • electronic energy
  • Rotational energy
  • All of these

37. Moment of inertia depends on

  • Distribution of particles
  • Mass
  • Position of axis of rotation
  • All of these

38. A body of M.I. 3 kg m² rotating with an angular velocity 2 rad/s has the same K.E. as a mass of 12 kg moving with a velocity of

  • 1 m/s
  • 2 m/s
  • 4 m/s
  • 8 m/s

39. The product of the force times the lever arm; the movement of the force about the axis is:

  • torque
  • lever arm
  • rotational inertia
  • angular momentum

40. The dimensions of angular momentum are

  • [M1 L2 T-1]
  • [M1 L1 T-1]
  • [M1 L1 T-2]
  • [M1 L2 T-2]

41. The M.I. of a body does not depends upon

  • Angular velocity of a body
  • Axis of rotation of the body
  • The mass of the body
  • The distribution of the body

42. A body with a definite shape that doesn't change is:

  • period
  • angular acceleration
  • rigid body
  • radius of gyration

43. A dancer on ice spins faster when she folds here arms. This is due to

  • Increases in energy and increase in angular momentum
  • Decrease in friction at the skates
  • Constant angular momentum and increase in kinetic energy
  • Increase in energy an decreases in angular momentum

44. Two circular discs A and B have equal masses and uniform thickness but have densities ρ1 and ρ2 such that ρ1 >ρ2. their moment of inertia is

  • I1 > I2
  • I1 >> I2
  • I1 < I2
  • I1 = I2

45. Centripetal acceleration is directed

  • directed away from the center of the circle
  • directed towards the center of the circle
  • it is perpendicular to the radius at that point
  • It has no direction

46. The relation between linear velocity and angular velocity

  • r = v⍵
  • ⍵ = vr
  • v = r⍵
  • a = v⍵

47. A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration?

  • 0.01 rad/s/s
  • 0.05 rad/s/s
  • 1.8 rad/s/s
  • 2.6 rad/s/s

48. A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

  • 9.6 rad/s/s
  • 4.8 rad/s/s
  • 3.1 rad/s/s
  • 1.6 rad/s/s

49. Which of the following is the unit for centripetal force?

  • J
  • m/s2
  • kg⋅m/s
  • N

50. Centripetal acceleration is ...

  • Acceleration toward the center of a curved or circular path
  • Acceleration toward the outside of a circle
  • Vertical motion instead of horizontal motion
  • All of above

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