2024-25 - Test review - Uniform circular motion

Vocabulary

  • Uniform Circular Motion: Motion in a circular path at a constant speed.

  • Period: The time taken for one complete cycle of motion.

  • Frequency: The number of cycles per unit time.

  • Tangential Velocity: The linear speed of any point on a rotating object.

  • Centripetal Acceleration/Centripetal Force: Acceleration/force directed towards the center of the circular path.

  • Radial Forces: Forces acting along the radius of a circular path.

  • Universal Gravitation: The force of attraction between any two masses.

  • Center of Mass: The average position of all mass in a system.

  • Simple Harmonic Motion: Motion that repeats itself in a periodic manner.

Conceptual Questions

  1. Units:

    • Angular velocity: radians/second

    • Angular acceleration: radians/second²

    • Torque: Newton-meters (N·m)

    • Moment of inertia: kg·m²

    • Angular momentum: kg·m²/s

  2. Tangential: Refers to motion or acceleration that is at a right angle to the radius.

  3. Direction in Uniform Circular Motion: Velocity is tangent to the circular path, acceleration points toward the center.

  4. Equations:

    • Period of a spring mass (T) = 2π√(m/k)

    • Period of a pendulum (T) = 2π√(l/g)

  5. Pendulum Period with Length Doubling: The period increases (T is proportional to √l).

  6. Doubling Radius with Constant Period: Centripetal acceleration decreases by half, centripetal force also decreases by half.

  7. Penny on Turntable with Decreased Period: It moves outward until it loses contact; the limit period is calculated based on friction and centripetal force.

  8. Distance Traveled by Bicycle: Uses angular velocity multiplied by time to find linear distance.

  9. Locating Center of Mass: Balance point or average position of mass.

  10. Kepler’s 3 Laws:

  • 1st Law: Planets orbit in ellipses with the sun at one focus.

  • 2nd Law: A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.

  • 3rd Law: The square of the period of a planet is proportional to the cube of the semi-major axis of its orbit.

  1. Period for Distance 9r: T is proportional to √(r^3), thus period increases by a factor of √9 (or 3 times).

  2. Speed in Orbit: A planet moves fastest at perihelion (closest point to the sun).