A worked-example animation covering three physics problems on uniform circular motion. It walks through calculating linear speed from radius and period, finding spring force and centripetal acceleration for a mass on a spring, and deriving period, frequency, angular speed, and linear speed from given motion data. Each step shows the formula, substituted values, and final boxed answer, making it useful for students reviewing circular motion equations before exams or quizzes.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
Scene 1On-Screen Title: Problem 1: Linear Speed in Circular MotionQuestion: A ball moves in a horizontal circular motion with a radius of $0.20\text{ m}$ and a period of $0.50\text{ s}$. Calculate its linear speed. Answer:Formula: $v = \frac{2\pi r}{T}$ Calculation: $v = \frac{2 \times \pi \times 0.20}{0.50} = \mathbf{2.51\text{ m/s}}$ Scene 2On-Screen Title: Problem 2: Spring Force, Speed, and Centripetal AccelerationQuestion: A ball of mass $0.50\text{ kg}$ is attached to a spring and moves in uniform circular motion on a smooth horizontal surface ($k = 20\text{ N/m}$, $L_0 = 0.15\text{ m}$, $L = 0.25\text{ m}$). Find: (a) Elastic force, (b) Speed, (c) Centripetal acceleration. Answer:(a) Elastic force: $F = k(L - L_0) = 20(0.25 - 0.15) = \mathbf{2.0\text{ N}}$ (b) Speed: $v = \sqrt{\frac{F \cdot r}{m}} = \sqrt{\frac{2.0 \times 0.25}{0.50}} = \mathbf{1.0\text{ m/s}}$ (c) Centripetal acceleration: $a_c = \frac{v^2}{r} = \frac{1.0^2}{0.25} = \mathbf{4.0\text{ m/s}^2}$ Scene 3On-Screen Title: Problem 3: Period, Frequency, Angular and Linear SpeedQuestion: An object undergoes uniform circular motion, completing 20 periods in $5.0\text{ s}$ along a circle of radius $0.20\text{ m}$. Find: (a) Period, (b) Frequency, (c) Angular speed, (d) Linear speed. Answer:(a) Period ($T$): $T = \frac{5.0}{20} = \mathbf{0.25\text{ s}}$ (b) Frequency ($f$): $f = \frac{1}{T} = \frac{1}{0.25} = \mathbf{4.0\text{ Hz}}$ (c) Angular speed ($\omega$): $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.25} \approx \mathbf{25.13\text{ rad/s}}$ (d) Linear speed ($v$): $v = \omega r = 25.13 \times 0.20 \approx \mathbf{5.03\text{ m/s}}$ IMPORTANT LANGUAGE RULE: All on-screen text must be in Arabic EXCEPT mathematical equations, formulas, laws, symbols, variables, and numerical expressions. Keep every equation, formula, and law exactly as provided, without translating or changing it. Translate only the explanatory text, headings, labels, and descriptions into Arabic. Arabic text must use proper RTL direction and correct Arabic typography. Do not use English text anywhere else on the screen. Audience: student