Lesson test: Rotation

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Rotation

1.[2p]
A wheel starts from rest with a constant angular acceleration of 3.0 rad s⁻² for 6.0 s. Through how many radians does it turn?

CorrectNot quite: 54

2.[2p]
A point 0.25 m from the axis of a body spinning at 40 rad s⁻¹ moves how fast, in metres per second?

CorrectNot quite: 10

3.[2p]
Why does the moment of inertia depend on the axis chosen, while mass does not?

It weights each element of mass by the square of its distance from that axis

Correct

It is measured in different units about different axes

The answer is: It weights each element of mass by the square of its distance from that axis

Mass is conserved and moment of inertia is not

The answer is: It weights each element of mass by the square of its distance from that axis

It is defined only for symmetric bodies

The answer is: It weights each element of mass by the square of its distance from that axis

4.[2p]
A uniform disc of mass 8.0 kg and radius 0.30 m spins about its axis. What is its moment of inertia, in kg m²?

CorrectNot quite: 0.36

5.[3p]
A uniform rod of mass 2.0 kg and length 1.2 m has $I = M L^{2} / 12$ about its centre. What is its moment of inertia about a perpendicular axis through one end, in kg m²?

CorrectNot quite: 0.96

6.[2p]
For a given body, the moment of inertia is smallest about an axis through its centre of mass.

True

Correct

False

The answer is: True

7.[3p]
A hoop, a solid disc and a solid sphere roll from rest down the same slope. Which reaches the bottom first?

The solid sphere, because it has the smallest moment of inertia for its mass and radius

Correct

The hoop, because all its mass is at the rim

The answer is: The solid sphere, because it has the smallest moment of inertia for its mass and radius

They arrive together, since mass and radius cancel

The answer is: The solid sphere, because it has the smallest moment of inertia for its mass and radius

The heaviest one

The answer is: The solid sphere, because it has the smallest moment of inertia for its mass and radius

8.[3p]
A flywheel of moment of inertia 25 kg m² spins at 314 rad s⁻¹. What is its kinetic energy, in megajoules?

CorrectNot quite: 1.23

9.[3p]
Match each body to its moment of inertia about the stated axis, as a multiple of $M R^{2}$ or $M L^{2}$ .

Thin hoop about its axis
Solid disc about its axis
Solid sphere about a diameter
Uniform rod about its centre

one twelfth ML squared
MR squared
half MR squared
two fifths MR squared

Show the answer

Thin hoop about its axis: MR squared Solid disc about its axis: half MR squared Solid sphere about a diameter: two fifths MR squared Uniform rod about its centre: one twelfth ML squared

1.[2p] A wheel starts from rest with a constant angular acceleration of 3.0 rad s⁻² for 6.0 s. Through how many radians does it turn?

2.[2p] A point 0.25 m from the axis of a body spinning at 40 rad s⁻¹ moves how fast, in metres per second?

3.[2p] Why does the moment of inertia depend on the axis chosen, while mass does not?

4.[2p] A uniform disc of mass 8.0 kg and radius 0.30 m spins about its axis. What is its moment of inertia, in kg m²?

5.[3p] A uniform rod of mass 2.0 kg and length 1.2 m has I=ML2/12 about its centre. What is its moment of inertia about a perpendicular axis through one end, in kg m²?

6.[2p] For a given body, the moment of inertia is smallest about an axis through its centre of mass.

7.[3p] A hoop, a solid disc and a solid sphere roll from rest down the same slope. Which reaches the bottom first?

8.[3p] A flywheel of moment of inertia 25 kg m² spins at 314 rad s⁻¹. What is its kinetic energy, in megajoules?

9.[3p] Match each body to its moment of inertia about the stated axis, as a multiple of MR2 or ML2.

1.[2p]
A wheel starts from rest with a constant angular acceleration of 3.0 rad s⁻² for 6.0 s. Through how many radians does it turn?

2.[2p]
A point 0.25 m from the axis of a body spinning at 40 rad s⁻¹ moves how fast, in metres per second?

3.[2p]
Why does the moment of inertia depend on the axis chosen, while mass does not?

4.[2p]
A uniform disc of mass 8.0 kg and radius 0.30 m spins about its axis. What is its moment of inertia, in kg m²?

5.[3p]
A uniform rod of mass 2.0 kg and length 1.2 m has $I = M L^{2} / 12$ about its centre. What is its moment of inertia about a perpendicular axis through one end, in kg m²?

6.[2p]
For a given body, the moment of inertia is smallest about an axis through its centre of mass.

7.[3p]
A hoop, a solid disc and a solid sphere roll from rest down the same slope. Which reaches the bottom first?

8.[3p]
A flywheel of moment of inertia 25 kg m² spins at 314 rad s⁻¹. What is its kinetic energy, in megajoules?

9.[3p]
Match each body to its moment of inertia about the stated axis, as a multiple of $M R^{2}$ or $M L^{2}$ .