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Science lesson plan · 12th grade (Year 13 in England) · 30 minutes

Circular motion and centripetal force

Forces and motion

CCSS NGSS.HS-PS2-1CCSS NGSS.HS-PS2-4England: A level Physics: Circular motion (extension)

Objective and success criteria

Students will: Circular motion and centripetal force.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Orbits and orbital speed (v = 2Ï€r / T); Force, mass and acceleration (F = ma)

Leads to: the next skill in this area.

Materials: Force meters, Toy cars and ramps, Mini whiteboards, A diagram or short video clip of the idea, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Orbits and orbital speed (v = 2Ï€r / T); Force, mass and acceleration (F = ma)). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A geostationary satellite orbits at a radius of about 42160 km from Earth's centre, taking 1436 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place) → 3.1 km/sPrompt: Convert the period to seconds.
  2. What resultant force is needed to accelerate a 2 kg mass at 4 m/s²? → 8 NPrompt: F = m × a
  3. A satellite moves at a steady speed in a circular orbit. Why is it accelerating? (Its speed increases every orbit / Its direction is always changing, so its velocity changes / Its engines are always on / It is not accelerating) → Its direction is always changing, so its velocity changesPrompt: Velocity is a vector.

Hook · 3 min

  • Drop a sheet of paper and a scrunched-up sheet together and ask why one falls faster.
  • Share the objective: Circular motion and centripetal force. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A 1 kg object moves in a circle of radius 2 m at 5 m/s. What centripetal force is needed, in N? (F = m v² ÷ r)
  • Step 1: 1 × 5² ÷ 2 = 12.5
  • Step 2: So the answer is: 12.5 N
  • Answer: 12.5 N
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. A 1200 kg object moves in a circle of radius 1 m at 20 m/s. What centripetal force is needed, in N? (F = m v² ÷ r) → 480000 NPrompt: Square the speed first.
  2. Friction between the tyres and the road provides 16875 N of centripetal force for a 1500 kg car on a bend of radius 20 m. What is the car's speed, in m/s? → 15 m/sPrompt: Rearrange: v² = F r ÷ m.

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Friction between the tyres and the road provides 7500 N of centripetal force for a 1500 kg car on a bend of radius 20 m. What is the car's speed, in m/s? → 10 m/sPrompt: Rearrange: v² = F r ÷ m.
  2. A 60 kg object moves in a circle of radius 10 m at 4 m/s. What centripetal force is needed, in N? (F = m v² ÷ r) → 96 NPrompt: Square the speed first.

Watch out for

  • Everyday meanings of words getting in the way of the science meaning: define key words explicitly.
  • Remembering facts without the reason: ask "why?" and "what is the evidence?"

Support and stretch

Support

  • Review first: Orbits and orbital speed (v = 2Ï€r / T).
  • Use concrete materials: force meters.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/science/grade-12.

Free lesson plan from eurekami.com/lesson-plan-builder

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Circular motion and centripetal force

Name

Date

Score/ 6

  1. Question 1

    A 1200 kg object moves in a circle of radius 10 m at 15 m/s. What centripetal force is needed, in N? (F = m v² ÷ r)

    AnswerN

  2. Question 2

    A hammer thrower lets go of the hammer. Which way does it fly?

    • A. along a tangent to the circle at the point of release
    • B. straight outwards from the centre
    • C. in a smaller circle
    • D. towards the centre

  3. Question 3

    Friction between the tyres and the road provides 3840 N of centripetal force for a 1500 kg car on a bend of radius 25 m. What is the car's speed, in m/s?

    Answerm/s

  4. Question 4

    A 60 kg object moves in a circle of radius 10 m at 10 m/s. What centripetal force is needed, in N? (F = m v² ÷ r)

    AnswerN

  5. Question 5

    A car goes round a bend twice as fast. How does the centripetal force needed change?

    • A. it stays the same
    • B. it halves
    • C. it becomes four times larger
    • D. it doubles

  6. Question 6

    Friction between the tyres and the road provides 4000 N of centripetal force for a 1000 kg car on a bend of radius 25 m. What is the car's speed, in m/s?

    Answerm/s

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Answer key: Circular motion and centripetal force

  1. 1. 27000 N

  2. 2. A. along a tangent to the circle at the point of release

  3. 3. 8 m/s

  4. 4. 600 N

  5. 5. C. it becomes four times larger

  6. 6. 10 m/s