Worksheet: Angular Momentum in Terms of Linear Momentum

In this worksheet, we will practice calculating the angular momentum of an object that is moving along a circular path from its instantaneous linear momentum.

Q1:

Which of the following is the correct unit of angular momentum?

  • A kg⋅m2/s
  • B kg⋅m/s
  • C kg⋅m2/s2
  • D kg2⋅m2/s
  • E kg⋅m2⋅s

Q2:

The figure shows an object with a mass 𝑚 and an instantaneous linear velocity 𝑣 . At which of the labeled points would the angular momentum of the object be greatest?

  • APoint B
  • BPoint C
  • CPoint E
  • DPoint A
  • EPoint D

Q3:

An object moves along a circular path with a radius of 12 m. The object has a tangential speed of 4.4 m/s and an angular momentum of 475.2 kg⋅m2/s. What is the mass of the object?

Q4:

The SI unit of angular momentum is kilogram meters squared per second (kg⋅m2/s). The SI unit of linear momentum is kilogram-meter per second (kg⋅m/s). If angular momentum is divided by linear momentum, what will the SI units of the resultant quantity be?

  • A s/m
  • B m/s
  • C1/m
  • D m2
  • E m

Q5:

An object moves along a circular path. The object has a linear momentum of 12 kg⋅m/s and an angular momentum of 57.6 kg⋅m2/s. What is the radius of the object’s circular path?

Q6:

The SI unit of angular momentum is kilogram meters squared per second (kg⋅m2/s). If angular momentum is divided by a length, what will the SI unit of the resultant quantity be?

  • A kg⋅m3/s
  • B kg⋅m/s
  • C kg/m⋅s
  • D kg⋅m/s2
  • E kg⋅m2/s

Q7:

A brick is swung around in a circle on the end of a rope. The brick has a linear momentum of 3.0 kg⋅m/s, and the rope is 2.0 m long. What is the magnitude of the angular momentum of the brick?

Q8:

A 2.0 kg cast iron weight is swung around in a circle at 1.5 m/s on the end of a rope. The rope has a length of 1.2 m. What is the magnitude of the angular momentum of the iron weight?

Q9:

A car is being driven around a circular road. The car has a mass of 2,300 kg, and the road has a radius of 40 m. If the car has an angular momentum of 7 . 3 6 × 1 0 kg⋅m2/s, what is its tangential speed?

Q10:

An object moves along a circular path. The object has a mass of 15 kg, a linear speed of 2.0 m/s, and an angular momentum of 84 kg⋅m2/s. What is the radius of the object’s circular path?

Q11:

The figure shows a snapshot in time of an object moving along a circular path. The circular path is not shown, but it may be centered on point 𝐴 or point 𝐵 . The object has a mass of 5.0 kg and, at the instant of the snapshot, has a linear velocity of 2.0 m/s in the positive 𝑦 -direction.

If the circular path were centered on point 𝐵 , what would the magnitude of the angular momentum of the object be?

If the circular path were centered on point 𝐴 , what would the magnitude of the angular momentum of the object be?

Q12:

The figure shows an object with a mass of 1.2 kg. At the instant shown, the object has a linear velocity of 3.0 m/s in the positive 𝑦 -direction. What is the magnitude of the angular momentum of the object around point 𝑃 at the instant shown? Give your answer to 4 significant figures.

Q13:

An electron is moving along a circular path in a magnetic field. The electron has a linear momentum of 2 . 7 3 × 1 0 kg⋅m/s and an angular momentum of 1 . 1 8 × 1 0 kg⋅m2/s. What is the radius of the electron’s path? Give your answer to 3 significant figures.

Q14:

The figure shows an object moving along a circular path around a point 𝑃 . What is the magnitude of the angular momentum of the object?

Q15:

The figure shows an object with a mass of 2.0 kg. At the instant shown, the object has a linear velocity of 1.4 m/s in the positive 𝑦 -direction. What is the magnitude of the angular momentum of the object around point 𝑃 at the instant shown?

Q16:

A coin in a washing machine is pressed up against the side of the drum as the drum spins very fast. The coin is moving along a circular path with a radius of 20 cm and has an angular momentum of 0.030 kg⋅m2/s. What is the magnitude of the linear momentum of the coin?

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