Practice Exam 3 - PHYS 221

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Questions and Answers

Using the kinematic equation, how does the displacement relate to initial velocity, acceleration, and time?

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

What does the equation $F = m\vec{a}$ represent in physics, and who formulated this law?

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

In the context of energy, how can the total mechanical energy be expressed mathematically?

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

Define the principle of conservation of energy in your own words.

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. Signup and view all the answers

How is the rotational kinetic energy defined in terms of moment of inertia?

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. Signup and view all the answers

Explain the concept of net force and its significance in motion.

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

What relationship does the equation $v_f^2 = v_0^2 + 2a \Delta r$ describe?

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

State the equation for work done by a force and its components.

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. Signup and view all the answers

Describe how angular acceleration is defined in relation to angular velocity.

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

What is the formula for calculating gravitational force between two masses?

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

Which system(s) will the mass first pass the equilibrium point when released from rest in mass and spring systems placed in different liquids with varying damping characteristics?

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

If an object is rolling without slipping in the positive î-direction but is slowing down, in what direction is its angular velocity vector ω⃗?

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

What information can be derived about the oscillation characterized by its period, amplitude, and maximum acceleration?

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 $a_{max} = rac{(2eta ext{π})^2}{T^2}$. Signup and view all the answers

How can you calculate the angular acceleration α⃗ of a system given its moment of inertia and the forces acting on the beams?

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. Signup and view all the answers

For an object with mass m, radius r, and moment of inertia I at height h0, if it rolls down a ramp and reaches $h_2 = 2h_1$, what is h0 in terms of m, r, I, g, and h2?

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

What dimensions should your answer to h0 have after confirming it is correct?

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

In the scenario where a clay ball drops onto a spinning pottery wheel, how would you find the new angular speed after the ball lands?

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

What fraction of the system’s rotational energy is lost when a clay ball sticks to the pottery wheel?

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

Flashcards

Equation for displacement

The change in position of an object.

Equation for velocity

Rate of change of displacement with respect to time.