Projectile Motion and Circular Motion

Name: Projectile Motion and Circular Motion
Author: StemPy Lab

A ball thrown at an angle goes up and down and forward at the same time. A stone on a string keeps its speed, and still it is accelerating. In this course we study the path, the time, the height and the range of a projectile, and we find the acceleration of a body in uniform circular motion, which points to the centre of the circle.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Projectile motion
A projectile moves under gravity alone. Its horizontal velocity never changes, and its vertical motion is free fall, with the acceleration $g$ downwards. On level ground, the time of flight is $T = \frac{2u\sin\theta}{g}$ , the greatest height is $H = \frac{u^2\sin^2\theta}{2g}$ , and the range is $R = \frac{u^2\sin 2\theta}{g}$ . The path is a parabola.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Range, height and the angle of projection
For a fixed launch speed on level ground, the range is largest at $45^\circ$ , where $R_{\max} = \frac{u^2}{g}$ . Two angles that add up to $90^\circ$ give the same range, but the steeper one goes higher and stays up longer. $\tan\theta = \frac{4H}{R}$ gives the launch angle from the height and the range. Landing above or below the start needs the full equation for $y$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Uniform circular motion
In uniform circular motion a body goes round a circle at a steady speed. Its velocity points along the circle and keeps turning, so it is accelerating. The acceleration points to the centre, with size $a = \frac{v^2}{r} = \omega^2 r$ , where $\omega = \frac{2\pi}{T}$ is the angular velocity and $v = \omega r$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Test Your Learning

Projectile and Circular Motion: Practice Paper

20 questions · 40 min

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More onMechanics › Vectors and Motion in a Plane Mechanics › Circular Motion

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Projectile Motion and Circular Motion

Course outline (3 lessons)