Review

Final Review for Phys 120

Question 1 Angular Momentum

• 

• The one question about throwing a ball at the pins

  • we are ignoring gravity
    • we are assuming that we are spinning the pin about the center of mass
      • like if the ball is force adding adding to it

  • 2 things are conservered

    • linear momentum $\vec{p}$
      • we know that ${\vec{p}}_i={\vec{p}}_f$
        • ⇒ m_{b}\vec{v}_{bi}=m_{a}\vec{v}_{o}+m_{b}\vec{v}_{bf}$$(0.603kg)(12.8m/s)=(0.383kg)\vec{v}_{o}+(0.453kg)(5.0m/s)
    • angular momentum $\vec{L}$
      • we know that ${\vec{L}}_i={\vec{L}}_f$
        • $\vec{r}\times {\vec{p}}_i=\vec{r}\times {\vec{p}}_f+{\vec{L}}_o$
          • $|\vec{r}\times {\vec{p}}_i|=rm{v}_i\sin \theta ⟹m{v}_{i}d$
            • d is the height of the ball hiting the center of mass
          • $m{v}_{bi}d=m{v}_{bf}d+I_o{w}_o$
            • we are adding I and W because we start with a initial velocity and we will end with a spinning object and a moving object so it “split”

Question 2 parallel axis theorem

• lecture 20 i cliccer question
  • sphere: $I_{cm}=\frac{2}{3}M{R}^2$
  • rod $I_r=\frac{1}{3}M{L}^3$
  • $I_{tot}=I_r+I_s$ we know what $I_r$ is not $I_s$
    • $I_s=I_{cm}+M{L}^2$
      • ⇒ $I_s=\frac{2}{5}M{R}^2+M{L}^2$
        • $I_{tot}=\frac{1}{3}M{L}^2+\frac{2}{3}M{R}^2+M{L}^2$

Question 3 Precession

Question 4 that one question on SHM part 2 b

• Question 1
  • A 2,671 g mass is hung on a “massless” vertical spring with a spring constant of k = 330 N/m. The mass is pulled down and released such that it undergoes simple harmonic motion with an amplitude of 10.0 cm. 
  • a) What is the spring potential energy of the system in Joules when the mass is located 6.7 cm below the equilibrium position (about which the mass oscillates)? 

• solve

  • we know its in eq $kx=mg\to x=\frac{mg}{k}$
    • $U_s=\frac{1}{2}k(x+d{)}^2$
• Question 2
  • The mass in part a) is now removed and a new 376 g mass is hung from the same spring (k = 330 N/m). This new mass is pulled down 7.60 cm below the equilibrium position and released. It starts undergoing simple harmonic motion. 
  • b) Find the velocity of the mass in m/s at t = 7.3 s. If the mass is moving upwards the velocity should be positive and if it is moving downwards the velocity should be negative. 

• solve

  • we know that d=A because how ever you pull it down it will go back that amount