Lesson test: Torque and angular momentum

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Torque and angular momentum

1.[2p]
A force of 120 N is applied perpendicular to a spanner 0.25 m from the bolt. What torque is applied, in newton metres?

CorrectNot quite: 30

2.[2p]
The same 120 N force is applied at 35° to a spanner 0.25 m long. What torque does it apply, in newton metres?

CorrectNot quite: 17.2

3.[3p]
Why does the angular momentum of a body under a central force never change?

A central force acts along the line to the centre, so its moment arm about that centre is zero

Correct

Central forces are always weak

The answer is: A central force acts along the line to the centre, so its moment arm about that centre is zero

The body moves in a circle, so its speed is constant

The answer is: A central force acts along the line to the centre, so its moment arm about that centre is zero

Angular momentum is conserved in every situation

The answer is: A central force acts along the line to the centre, so its moment arm about that centre is zero

4.[3p]
A skater with a moment of inertia of 4.0 kg m² spins at 1.5 rad s⁻¹ and pulls their arms in, reducing it to 1.6 kg m². What is the new angular velocity, in rad s⁻¹?

CorrectNot quite: 3.75

5.[2p]
The kinetic energy of a spinning skater is unchanged when they pull their arms in.

True

The answer is: False

False

Correct

6.[3p]
A 2.5 kg mass hangs from a cord wound round a uniform pulley of mass 1.5 kg. What is the acceleration of the mass, in m s⁻², with $g = 9.81$ m s⁻²?

CorrectNot quite: 7.55

7.[3p]
Which of Kepler's laws follows from angular momentum conservation alone, with no assumption about how gravity depends on distance?

The law of equal areas in equal times

Correct

The law that orbits are ellipses with the Sun at one focus

The answer is: The law of equal areas in equal times

The law relating the period to the semi-major axis

The answer is: The law of equal areas in equal times

None of them

The answer is: The law of equal areas in equal times

8.[3p]
Which of these are consequences of $\sum τ = d L / d t$ ?

Select all that apply

A helicopter needs a tail rotor to stop the fuselage turning

Correct

A diver tucks to somersault faster and opens out to slow down

Correct

A collapsing star spins up as its radius falls

Correct

A spinning body speeds up on its own if left alone

The answer is: A helicopter needs a tail rotor to stop the fuselage turning, A diver tucks to somersault faster and opens out to slow down, A collapsing star spins up as its radius falls

9.[2p]
Match each linear quantity to its rotational counterpart.

Force
Mass
Momentum
Acceleration

moment of inertia
angular acceleration
angular momentum
torque

Show the answer

Force: torque Mass: moment of inertia Momentum: angular momentum Acceleration: angular acceleration

1.[2p] A force of 120 N is applied perpendicular to a spanner 0.25 m from the bolt. What torque is applied, in newton metres?

2.[2p] The same 120 N force is applied at 35° to a spanner 0.25 m long. What torque does it apply, in newton metres?

3.[3p] Why does the angular momentum of a body under a central force never change?

4.[3p] A skater with a moment of inertia of 4.0 kg m² spins at 1.5 rad s⁻¹ and pulls their arms in, reducing it to 1.6 kg m². What is the new angular velocity, in rad s⁻¹?

5.[2p] The kinetic energy of a spinning skater is unchanged when they pull their arms in.

6.[3p] A 2.5 kg mass hangs from a cord wound round a uniform pulley of mass 1.5 kg. What is the acceleration of the mass, in m s⁻², with g=9.81 m s⁻²?

7.[3p] Which of Kepler's laws follows from angular momentum conservation alone, with no assumption about how gravity depends on distance?

8.[3p] Which of these are consequences of ∑τ=dL/dt?

9.[2p] Match each linear quantity to its rotational counterpart.

1.[2p]
A force of 120 N is applied perpendicular to a spanner 0.25 m from the bolt. What torque is applied, in newton metres?

2.[2p]
The same 120 N force is applied at 35° to a spanner 0.25 m long. What torque does it apply, in newton metres?

3.[3p]
Why does the angular momentum of a body under a central force never change?

4.[3p]
A skater with a moment of inertia of 4.0 kg m² spins at 1.5 rad s⁻¹ and pulls their arms in, reducing it to 1.6 kg m². What is the new angular velocity, in rad s⁻¹?

5.[2p]
The kinetic energy of a spinning skater is unchanged when they pull their arms in.

6.[3p]
A 2.5 kg mass hangs from a cord wound round a uniform pulley of mass 1.5 kg. What is the acceleration of the mass, in m s⁻², with $g = 9.81$ m s⁻²?

7.[3p]
Which of Kepler's laws follows from angular momentum conservation alone, with no assumption about how gravity depends on distance?

8.[3p]
Which of these are consequences of $\sum τ = d L / d t$ ?

9.[2p]
Match each linear quantity to its rotational counterpart.