Practice Test 10 - AP Physics C Mechanics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. Car A travels east at 30 m/s. Car B travels north at 40 m/s. What is the velocity of Car A as measured by an observer in Car B?
2. A satellite orbits Earth at a distance of $2R$ from Earth's center, where $R$ is Earth's radius. If the satellite's orbital radius is increased to $4R$, by what factor does the gravitational force on the satellite change?
3. A uniform rod of length $L$ and mass $M$ is pivoted at one end and can rotate freely in a vertical plane. The rod is initially horizontal and released from rest. When the rod has rotated through an angle $\theta$ from the horizontal, what is the gravitational potential energy of the rod relative to its initial position?
4. A circular platform of mass $M$ and radius $R$ is free to rotate friction-free about its center. A person of mass $m$ stands at the edge. The system is initially at rest. The person begins to walk along the edge with a speed $v$ relative to the platform. What is the magnitude of the angular velocity of the platform relative to the ground? The rotational inertia of the platform is $I_p = \frac{1}{2}MR^2$.
5. A mobile consists of two horizontal rods suspended by strings. The upper rod has mass $M_1 = 0.5\text{ kg}$ and length $L_1 = 1.0\text{ m}$. Two masses are attached to its ends: $m_1 = 2.0\text{ kg}$ on the left and $m_2 = 3.0\text{ kg}$ on the right. For the upper rod to be in rotational equilibrium, at what distance from the left end must the suspension string be attached?
6. The velocity of a particle in the xy-plane is given by $\vec{v}(t) = (4t)\hat{i} + (3t^2 - 1)\hat{j}$. What is the magnitude of the particle's acceleration at $t=1 \text{ s}$?
7. A composite system consists of a solid cylinder of mass $M$ and radius $R$ with its center at the origin, and a point mass $m$ located at distance $3R$ from the origin along the positive $x$-axis. What condition must be satisfied for the center of mass to be located at $x = R$?
8. Two planets, A and B, have the same density but planet B has twice the radius of planet A. If the surface gravitational field strength on planet A is $g_A$, what is the surface gravitational field strength on planet B?
9. A solid disk and a hoop have the same mass $M$ and radius $R$. They are both initially at rest and are free to rotate about a fixed, frictionless axle through their centers. The same constant net torque is applied to both. After one second, which of the following correctly compares their angular accelerations, $\alpha_{disk}$ and $\alpha_{hoop}$?
10. A particle's position is described by the vector $\vec{r}(t) = (R\cos(\omega t))\hat{i} + (2R\sin(\omega t))\hat{j}$, where $R$ and $\omega$ are positive constants. At which of the following times $t > 0$ are the particle's velocity and acceleration vectors first perpendicular to each other?
11. A system consists of two point masses: $m_1 = 2.0\text{ kg}$ at position $\vec{r_1} = (1, 2, 3)\text{ m}$ and $m_2 = 4.0\text{ kg}$ at position $\vec{r_2} = (4, -1, 2)\text{ m}$. What is the position vector of the center of mass?
12. A small solid sphere of radius $r$ rolls without slipping inside a large fixed hemispherical bowl of radius $R$, starting from rest at the same height as the center of the bowl. What is the speed of the sphere's center of mass at the bottom of the bowl?
13. The student-stool-wheel system is now rotating with a constant angular velocity. What can be concluded about the net torque on the system?
14. A torsion pendulum consists of a solid disk with rotational inertia $I$ attached to a wire with torsion constant $\kappa$. It oscillates with a period $T_0$. If the disk is replaced with a hoop of the same mass and radius, what is the new period? The rotational inertia of a hoop is twice that of a solid disk of the same mass and radius.
15. Using the information given, determine the object's acceleration at this point for a block sliding down a frictionless $30^\circ$ incline.
16. Using Kepler's third law, how does orbital period $T$ scale with orbital radius $r$ for satellites around Earth?
17. A simple pendulum and a physical pendulum, consisting of a uniform rod of length $L$ pivoted at one end, both have the same length $L$. How does the period of the rod, $T_{rod}$, compare to the period of the simple pendulum, $T_{simple}$?
18. A satellite is in an elliptical orbit around a planet. Which of the following quantities is conserved throughout the satellite's orbit?
19. A pendulum bob of mass $m$ is released from rest at a height $H$ above its lowest point. Air resistance is negligible. What is the kinetic energy of the bob as it passes through its lowest point?
20. A block of mass $m$ attached to a horizontal spring of constant $k$ is displaced from its equilibrium position by a distance $A$ and released from rest. What is the speed of the block when it is at a position $x = A/2$?

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