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Advanced
Mathematical
GQ

Suppose we wish to make a neutrally buoyant hollow sphere out of titanium (\(\rho = 4500 \text{kg/m}^3\)). If the sphere has an outer radius of \( 1.5 \) \( \text{m} \), what must be its inner radius?

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.

Beginner
Proportional Analysis
MCQ

Two uniform disks have the same mass but different radii: disk \( 1 \) has a radius \( R \) and disk \( 2 \) has a radius \( 2R \). What is the ratio of the moment of inertia of the first disk to the second disk?

Intermediate
Conceptual
GQ

Water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Without using equations, explain your answer.

Intermediate
Mathematical
FRQ

Divers in Acapulco jump from a cliff that is \( 36 \, \text{m} \) above the water with an initial vertical velocity of \( 2 \, \text{m/s} \).

Advanced
Mathematical
MCQ

A theme park ride consists of a large vertical wheel of radius \( R \) that rotates counterclockwise on a horizontal axle through its center. The cars on the wheel move at a constant speed \( v \). Points \( A \) and \( D \) represent the position of a car at the highest and lowest point of the ride, respectively. While passing point \( A \), a student releases a small rock of mass \( m \), which falls to the ground without hitting anything. Which of the following best represents the kinetic energy of the rock when it is at the same height as point \( D \)?

Beginner
Conceptual
MCQ

The displacement \( x \) of an object moving in one dimension is shown above as a function of time \( t \). The acceleration of this object must be

Intermediate
Mathematical
FRQ

A discus is held at the end of an arm that starts at rest. The average angular acceleration of \(54 \, \text{rad/s}^2 \) lasts for 0.25 s. The path is circular and has radius 1.1 m.

Note: A discuss is a heavy, flattened circular object for throwing.

Intermediate
Mathematical
GQ

How large must a heating duct be if air moving \( 3 \ \frac{\text{m}}{\text{s}} \) along it can replenish the air in a room of \( 300 \ \text{m}^3 \) volume every \( 15 \) minutes? Assume the air’s density remains constant.

Beginner
Conceptual
GQ

Does the odometer of a car measure a scalar or a vector quantity? What about the speedometer?

Intermediate
Proportional Analysis
MCQ

The exoplanet HD 69830b has a mass 10 times that of the Earth and a radius 5 times that of the Earth. The value of g on HD 69830b is most nearly

Intermediate
Mathematical
MCQ

Consider a rigid body that is rotating. Which of the following is an accurate statement?

Advanced
Proportional Analysis
GQ

Two identical satellites are placed in orbit of two different planets. Satellite \(A\) orbits Mars, and Satellite \(B\) orbits Jupiter. The orbital speeds of each satellite are the same. Which satellite has a greater orbital radius?

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?
Intermediate
Conceptual
MCQ

A rocket explodes into two fragments, one \(25\) times heavier than the other. The change in momentum of the lighter fragment is

Advanced
Mathematical
MCQ
Wagon Wheel Structure Moment of Inertia Wheel Mass Wheel Radius
Wagon \(A\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.5 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(B\) Solid disk \[\frac{1}{2} M R^2\] \[ 0.2 \, \text{kg} \] \[ 0.1 \, \text{m} \]
Wagon \(C\) Hollow hoop \[M R^2\] \[ 0.1 \, \text{kg} \] \[ 0.1 \, \text{m} \]

Three wagons have identical total mass (including their wheels) and each has four wheels. However, the wheels on each wagon have different designs with varying mass distributions and radii as shown in a reference chart. When accelerating each wagon from a standstill to \( 10 \) \( \text{m/s} \), which wagon requires the most energy input?

Intermediate
Mathematical
GQ

A major-league pitcher can throw a baseball in excess of \( 41.0 \, \text{m/s} \). If a ball is thrown horizontally at this speed, how much will it drop by the time it reaches a catcher who is \( 17.0 \, \text{m} \) away from the point of release?

Beginner
Conceptual
MCQ

A sled glides across ice and eventually stops. This stopping is best explained by ____.

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

An object of mass \( m = 3.0 \) \( \text{kg} \) is attached to one end of a string with negligible mass and length \( L = 0.80 \) \( \text{m} \). The object is released from rest at time \( t = 0 \), when the string is horizontal. At time \( t = t_1 \) the object is at the location shown in the figure, where the string is vertical. Which of the following is most nearly the magnitude of the tension in the string at time \( t = t_1 \)?

Intermediate
Mathematical
GQ

A \(5.0 \, \text{g}\) coin is placed \(15 \, \text{cm}\) from the center of a turntable. The coin has coefficients of static and kinetic friction of \(\mu_s = 0.80\) and \(\mu_k = 0.50\). The turntable slowly speeds up to \(60 \, \text{rpm}\). Does the coin slide off the turntable?

Advanced
Conceptual
MCQ

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

Beginner
Conceptual
MCQ

A person stands on a scale in an elevator. His apparent weight will be the greatest when the elevator

Beginner
Mathematical
MCQ

A student sets an object attached to a spring into oscillatory motion and uses a motion detector to record the velocity of the object as a function of time. The total change in the object’s speed between \(1.0 \, \text{s}\) and \(1.1 \, \text{s}\) is most nearly

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