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Intermediate
Mathematical
MCQ

A horizontal uniform rod of length L and mass M is pivoted at one end and is initially at rest. A small ball of mass M (same masses) is attached to the other end of the rod. The system is released from rest. What is the angular acceleration of the rod just immediately after the system is released?

Advanced
Conceptual
MCQ

A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?

\( \text{Solid sphere: } I = \frac{2}{5}mR^2, \quad \text{Solid disk: } I = \frac{1}{2}mR^2, \quad \text{Hoop: } I = mR^2 \)

Beginner
Conceptual
MCQ

What does distance represent during any type of motion?

Intermediate
Mathematical
MCQ

A plane, 220 meters high, is dropping a supply crate to an island below. It is traveling with a horizontal velocity of 150 m/s. At what horizontal distance must the plane drop the supply crate for it to land on the island? Use \( g = 9.81 \, m/s^2\).

Beginner
Mathematical
GQ

A stone is thrown horizontally at \(8.0 \, \text{m/s}\) from a cliff \(80 \,\text{m}\) high. How far from the base of the cliff will the stone strike the ground?

Intermediate
Conceptual
MCQ

A solid sphere \( \left( I = \frac{2}{5}MR^2 \right) \) and a solid cylinder \( \left( I = \frac{1}{2}MR^2 \right) \), both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is

Advanced
Conceptual
MCQ

In both cases, a massless rod is supported by a fulcrum, and a \(200 \, \text{kg}\) hanging mass is suspended from the left end of the rod by a cable. A downward force \(F\) keeps the rod in rest. The rod in Case A is \(50 \, \text{cm}\) long, and the rod in Case B is \(40 \, \text{cm}\) long (each rod is marked at \(10 \, \text{cm}\) intervals). The magnitude of each vertical force \(F\) exerted on the rod will be

Intermediate
Proportional Analysis
MCQ

A car with speed \( v \) and an identical car with speed \( 3v \) both travel the same circular section of an unbanked (flat) road. If the frictional force required to keep the faster car on the road without skidding is \( F \), then the frictional force required to keep the slower car on the road without skidding is

Advanced
Mathematical
GQ

A \(4 \, \text{kg}\) mass is traveling at \(10 \, \text{m/s}\) to the right when it collides inelastically with a stationary \(7 \, \text{kg}\) mass. The \(7 \, \text{kg}\) mass then travels at \(2 \, \text{m/s}\) at an angle of \(22^\circ\) below the horizontal. What are the velocity and the angle of the \(4 \, \text{kg}\) mass?

Beginner
Mathematical
MCQ

The total energy of a system in SHM is given by \( E \). At what displacement from equilibrium is the kinetic energy equal to the potential energy?

Intermediate
Mathematical
GQ

There are two cables that lift an elevator, each with a force of \(10{,}000 \, \text{N}\). The \(1{,}000 \, \text{kg}\) elevator is lifted from the first floor and accelerates over \(10 \, \text{m}\) until it reaches its top speed of \(6 \, \text{m/s}\). What is the mass of the people in the elevator?

Intermediate
Conceptual
MCQ

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

Beginner
Mathematical
GQ

A hypothetical planet has a radius \( 2.0 \) times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

Intermediate
Mathematical
MCQ

A rod of length \( L \) is rotated about its center with \( I = \frac{ML^{2}}{12} \). What is the moment of inertia at either end of the rod?

Intermediate
Conceptual
GQ

An object has a mass of 10 kg. For each case below answer the questions and provide an example.

  1. If an object is moving, is it possible for the net force acting on it to be zero?
  2. If the acceleration of an object is zero, are no forces acting on it?
  3. Only one force acts on an object. Can the object have zero acceleration?
  4. Only one force acts on an object. Can it have zero velocity?
Advanced
Proportional Analysis
MCQ

Two satellites are in circular orbits around Earth. Satellite A has speed \(v_A\). Satellite B has an orbital radius nine times that of satellite A. What is the speed of satellite B?

Intermediate
Mathematical
GQ

A person is trying to judge whether a picture (mass = 1.42 kg) is properly positioned by temporarily pressing it against a wall. The pressing force is perpendicular to the wall. The coefficient of static friction between the picture and the wall is 0.62. What is the minimum amount of pressing force that must be used?

Advanced
Proportional Analysis
MCQ

A rocket of mass \( m \) is launched with kinetic energy \( K_0 \), from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii? Give your answer in terms of the gravitational constant \( G \), the mass of the Earth \( m_E \), the radius of the Earth \( R_E \), and the mass of the rocket?

Intermediate
Conceptual
GQ

If you stand on a bathroom scale in a moving elevator, does its reading change?

Advanced
Mathematical
FRQ
A physical setup diagram showing a tall vertical tower with a pivot point at the top. A single chain of length 10 meters hangs from the pivot, connected to a chair. The chair and chain are drawn at an angle theta from the vertical. The child is depicted as a simplified block sitting in the chair. A dashed circular path is drawn indicating the radius of rotation of the chair. A horizontal dimension line indicates the radius r, and an arc marker labels the angle theta between the vertical tower and the taut chain.

A neighbor’s child wants to go to a carnival to experience the wild rides. The neighbor is worried about safety because one of the rides looks particularly dangerous. She knows that you have taken physics and so asks you for advice. The ride in question has a \(4 \, \text{kg}\) chair which hangs freely from a \(10 \, \text{m}\) long chain attached to a pivot on the top of a tall tower. When the child enters the ride, the chain is hanging straight down. The child is then attached to the chair with a seat belt and shoulder harness. When the ride starts up, the chain rotates about the tower. Soon the chain reaches its maximum speed and remains rotating at that speed, which corresponds to one rotation about the tower every \(3 \, \text{seconds}\). When you ask the operator, he says the ride is perfectly safe. He demonstrates this by sitting in the stationary chair. The chain creaks but holds, and he weighs \(90 \, \text{kg}\).

Intermediate
Mathematical
FRQ

The occupants of a car traveling at a speed of \( 30 \) \( \text{m/s} \) note that on a particular part of a road their apparent weight is \( 15\% \) higher than their weight when driving on a flat road.

Intermediate
Mathematical
FRQ

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a 50 km diameter circular orbit with a period of 11 days.

Advanced
Conceptual
MCQ

A cart begins to move from rest on a horizontal track. Which of the following correctly indicates the magnitude of the average velocity of the cart during the interval shown and provides a valid explanation?

Hint: when solving this, its consider that the area of the acceleration vs time graph tells you the change in velocity.

Beginner
Mathematical
GQ

A person stands on a scale in an elevator. If the scale reads \( 600 \, \text{N} \) when that person is riding upward at a constant velocity of \( 4 \, \text{m/s} \), what is the scale reading when the elevator is at rest? Hint: The reading on the scale is simply the normal force.

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