Question
Solution
Common Misconception: The Hubble law suggests a privileged center.
Physical Resolution: Homogeneity and isotropy (Cosmological Principle).
Analogy: On a 2D sphere expanding uniformly, no point is the true center. Galaxies are not moving through space; the space between them is stretching.
Important nuance: For very distant galaxies ((z > 0.1)), the simple (v = H_0 d) breaks down; we must use general relativistic distances (luminosity distance, angular diameter distance) and consider cosmic deceleration/acceleration.
Run through the "Big Three" before writing a single equation: physics galaxy discussion questions solutions
Question
Solution
Below is a structured, detailed post of discussion questions and step-by-step solutions inspired by a typical "Physics Galaxy" style (conceptual depth, problem variety, worked examples). Topics cover mechanics, electromagnetism, waves, modern physics, and problem-solving strategies. Use as a study guide, classroom handout, or video script.
Discussion Question 3
A solid sphere of mass (M) and radius (R) is gently placed on a rough horizontal surface with initial center-of-mass velocity (v_0) and no initial angular velocity. Describe the subsequent motion. Find time when pure rolling starts and the final velocity. Question
Solution
Initial: slipping ⇒ kinetic friction (f_k = \mu_k M g) acts backward at contact point.
Linear deceleration: (a_cm = -\mu_k g).
Torque about CM: (\tau = f_k R = \mu_k M g R = I \alpha) with (I = \frac25 M R^2) ⇒ (\alpha = \frac5\mu_k g2R).
Angular velocity grows: (\omega(t) = \alpha t).
Velocity: (v(t) = v_0 - \mu_k g t).
Pure rolling when (v(t) = \omega(t) R):
[
v_0 - \mu_k g t = \frac5\mu_k g2R t \cdot R
]
[
v_0 - \mu_k g t = \frac5\mu_k g2 t
]
[
v_0 = \mu_k g t \left(1 + \frac52\right) = \frac72 \mu_k g t
]
[
t_r = \frac2 v_07 \mu_k g
]
Final velocity: (v_f = v_0 - \mu_k g t_r = v_0 - \mu_k g \cdot \frac2 v_07 \mu_k g = v_0 - \frac2 v_07 = \frac57 v_0). Solution
Discussion: Note that (v_f < v_0) and independent of (R). Interesting: If instead of solid sphere, a hollow sphere ((I = \frac23 M R^2)) is used, final velocity = (\frac56 v_0) (check — good discussion problem).
Why do galaxy rotation curves remain flat at large radii, and what does this imply about Newtonian gravity on galactic scales?
Scenario: A point charge $+Q$ is placed near an isolated neutral conductor. The conductor is then grounded. Discuss: Does the charge on the conductor become negative, or does it become zero?
The Physics Galaxy Solution: