Grade 12 Physics Unit 2 : Two-Dimensional Motion

This unit 2 expands on your study of kinematics by exploring motion in a plane, where objects move along curved paths. You’ll analyze the arcing flight of projectiles, the spinning of rotating objects, and the majestic orbits of planets, tying them all together with Newton’s universal law.

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Chapter 2.1 – Projectile motion

This chapter breaks down the motion of any object thrown or launched into the air.

• Define projectile motion as the movement of an object under the sole influence of gravity.
• Understand the key principle: the horizontal and vertical components of the motion are independent.
• Analyze the motion by treating the horizontal component as constant velocity and the vertical component as constant acceleration (due to gravity, g).
• Calculate key quantities like the maximum height, time of flight, and range of a projectile. .

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Chapter 2.2 & 2.3 – Rotational Motion and Dynamics

Explore the physics of spinning objects, from car wheels to planets.

• Describe rotational motion using angular variables like angular displacement (θ), angular velocity (ω), and angular acceleration (α).
• Define torque (τ) as the rotational equivalent of force—the “twist” that causes an object to rotate.
• Understand moment of inertia (I) as a measure of an object’s resistance to changes in its rotational motion (rotational mass).
• Apply the rotational version of Newton’s Second Law.

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Chapter 2.4 – Planetary motion and Kepler’s laws

This section focuses on the rules that govern the orbits of planets, moons, and satellites.

• State and explain Kepler’s Three Laws of Planetary Motion:
  1. The Law of Orbits: Planets orbit the Sun in ellipses, not perfect circles.
  2. The Law of Areas: A planet moves fastest when it is closest to the Sun.
  3. The Law of Periods: There is a precise mathematical relationship between a planet’s distance from the Sun and the time it takes to orbit.

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Chapter 2.5 – Newton’s law of universal Gravitation

Discover the fundamental force that explains why planets move the way they do.

• State Newton’s Law of Universal Gravitation, which describes the force of attraction between any two objects with mass.
• Use the universal gravitation formula to calculate the gravitational force between two bodies.
• Understand how Newton’s law provides the underlying physical explanation for Kepler’s empirically derived laws.

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Learning Outcomes

By the end of this unit 2, you’ll be able to:

• Describe the motion of objects in horizontal and inclined projectiles.
• Explain uniform rotational motion and rotational dynamics.
• State and apply Kepler’s laws of planetary motion.
• Describe and use Newton’s law of Universal Gravitation to solve problems.