Practice Exam 3 - PHYS 221

Displacement is given by the equation $\vec{r} = \vec{r}_0 + \vec{v}_0 t + \frac{1}{2} \vec{a} t^2$.

'F = m\vec{a}$ represents Newton's second law of motion, which states that force equals mass times acceleration.

Total mechanical energy can be expressed as $E = K + U$, where $K$ is kinetic energy and $U$ is potential energy.

<p>The principle of conservation of energy states that energy in a closed system cannot be created or destroyed but can only be transformed from one form to another.</p> Signup and view all the answers

<p>Rotational kinetic energy is defined as $K_R = \frac{1}{2} I \omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.</p> Signup and view all the answers

<p>Net force is the vector sum of all forces acting on an object and determines the object's acceleration and motion.</p> Signup and view all the answers

<p>This equation relates the final velocity, initial velocity, acceleration, and displacement of an object under uniform acceleration.</p> Signup and view all the answers

<p>The work done by a force is given by $dW = \vec{F} \cdot d\vec{r}$, where $\vec{F}$ is the force and $d\vec{r}$ is the displacement.</p> Signup and view all the answers

<p>Angular acceleration is defined as $\alpha = \frac{d\omega}{dt}$, the rate of change of angular velocity with respect to time.</p> Signup and view all the answers

<p>The gravitational force between two masses is given by $\vec{F}_G = -G \frac{m_1 m_2}{r^2} \hat{r}$.</p> Signup and view all the answers

<p>Only system A, which is under damped, will have the mass first pass the equilibrium point.</p> Signup and view all the answers

<p>The angular velocity vector ω⃗ will still point in the positive k̂-direction.</p> Signup and view all the answers

<p>The period is the time taken for one complete cycle, the amplitude is the maximum displacement from equilibrium, and maximum acceleration is determined by the equation $a_{max} = rac{(2eta ext{π})^2}{T^2}$.</p> Signup and view all the answers

<p>Angular acceleration α⃗ can be calculated using the equation α = $rac{ au}{I}$, where τ is the net torque and I is the moment of inertia.</p> Signup and view all the answers

<p>h0 can be expressed as $h_0 = h_2 + rac{I}{mr}h_2$.</p> Signup and view all the answers

<p>The dimensions of h0 should be in units of length (meters).</p> Signup and view all the answers

<p>The new angular speed can be found using conservation of angular momentum: $I_{total}ω_{final} = I_{wheel}ω_{initial} + I_{clay}ω_{clay}$.</p> Signup and view all the answers

<p>The fraction of lost rotational energy can be calculated as $rac{E_{initial} - E_{final}}{E_{initial}}$.</p> Signup and view all the answers