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Advanced
Mathematical
MCQ

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

Advanced
Mathematical
GQ

A \(2.2 \times 10^{21} \, \text{kg}\) moon orbits a distant planet in a circular orbit of radius \(1.5 \times 10^8 \, \text{m}\). It experiences a \(1.1 \times 10^{19} \, \text{N}\) gravitational pull from the planet. What is the moon’s orbital period in Earth days?

Intermediate
Mathematical
FRQ

A 0.035 kg bullet moving horizontally at 350 m/s embeds itself into an initially stationary 0.55 kg block. Air resistance is negligible.

Advanced
Mathematical
FRQ

A pulley system consists of two blocks of mass \( 5 \) \( \text{kg} \) and \( 10 \) \( \text{kg} \), connected by a rope of negligible mass that passes over a pulley of radius \( 0.1 \) \( \text{m} \) and mass \( 2 \) \( \text{kg} \). The pulley is free to rotate about its axis. The system is released from rest, and the block of mass \( 10 \) \( \text{kg} \) starts to move downwards. Assume the pulley has a frictional force of \(5.7\) Newtons acting on the outer edge of the pulley.

Advanced
Mathematical
GQ

A \( 35 \) \( \text{kg} \) suitcase rests on a luggage‑loading ramp inclined \( 30.0^\circ \) above the horizontal. To keep it from sliding, a baggage‑handler pushes straight into the ramp (perpendicular to the surface) with a force of \( 45 \) \( \text{N} \). Find the coefficient of static friction \( \mu_s \) between the suitcase and the ramp.

Intermediate
Mathematical
GQ

A ball is kicked horizontally off a 20 m tall cliff at a speed of 11 m/s. What is the final velocity of the ball right before it hits the ground?

Intermediate
Mathematical
FRQ

A rocket, initially at rest, is fired vertically upward with an acceleration of \( 12.0 \, \text{m/s}^2 \). At an altitude of \( 1.00 \, \text{km} \), the rocket engine cuts off. Drag is negligible.

Advanced
Mathematical
FRQ

A conical pendulum is formed by attaching a ball of mass \( m \) to a string of length \( L \), then allowing the ball to move in a horizontal circle of radius \( R \).

Intermediate
Mathematical
GQ

A loop-de-loop roller coaster has a radius of \( 30 \) \( \text{m} \). Determine the apparent weight a \( 500 \) \( \text{N} \) person will feel at the bottom of the loop while traveling at a speed of \( 25 \) \( \text{m/s} \) and at the top of the loop while traveling at a speed of \( 20 \) \( \text{m/s} \).

Advanced
Mathematical
MCQ

A boy of mass \( m \) and a girl of mass \( 2m \) are initially at rest at the center of a frozen pond. They push each other so that she slides to the left at speed \( v \) across the frictionless ice surface and he slides to the right. What is the total work done by the children?

Intermediate
Mathematical
MCQ
The diagram shows a horizontally oriented circular pipe of initial diameter labeled ( D ) that bends smoothly upward into an S-shape and then levels off into a horizontal section whose diameter is labeled ( 2D ). On the lower horizontal section, a point on the pipe’s centerline is marked with a solid black dot and labeled "A". A right-pointing horizontal arrow originates at point A and is labeled ( v_0 ), indicating the fluid velocity at that point. Directly above point A, a dashed horizontal reference line extends across the page. A second dashed horizontal line, parallel to the first, is drawn through a point on the upper horizontal pipe section. The vertical distance between the two dashed lines is marked by a vertical bracket with arrowheads at both ends and labeled ( H ). On the upper horizontal pipe section, a solid black dot on the centerline is labeled "B". A vertical bracket on the left side of the lower dashed line shows the pipe diameter at A labeled ( D ). A similar bracket on the right side of the upper dashed line shows the pipe diameter at B labeled ( 2D ). All pipe walls are drawn as thin parallel curves representing the interior and exterior surfaces.

Water of density \( \rho \) flows through the section of circular pipe shown in the figure. At Point A, where the diameter of the pipe is \( D \), the water has a pressure \( P_0 \) and velocity \( v_0 \). Point B is located a vertical distance \( H \) above Point A in a section of the pipe that has diameter \( 2D \).

Which of the following expressions is equal to the pressure of the water at Point B?

Beginner
Conceptual
MCQ

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?

Beginner
Mathematical
MCQ

When a fan is turned off, its angular speed decreases from \( 10 \) \( \text{rad/s} \) to \( 6.3 \) \( \text{rad/s} \) in \( 5.0 \) \( \text{s} \). What is the magnitude of the average angular acceleration of the fan?

Intermediate
Conceptual
MCQ

Which of the following must be zero if an object is spinning at a constant rate? There may be more than one right answer.

Advanced
Mathematical
GQ

Two workers are holding a thin plate with length \(5 \, \text{m}\) and height \(2 \, \text{m}\) at rest by supporting the plate in the bottom corners. The workers are standing at rest on a slope of \(10^\circ\). Treat these supporting forces as vertical normal forces and calculate their magnitudes and state if both workers are sharing “the job” fairly.

Advanced
Proportional Analysis
GQ

A man weighing \( 700 \) \( \text{N} \) and a woman weighing \( 400 \) \( \text{N} \) have the same momentum. What is the ratio of the man’s kinetic energy \( K_m \) to that of the woman \( K_w \)?

Intermediate
Mathematical
MCQ

A soccer ball is kicked horizontally off an \( 85 \) \( \text{m} \) high cliff at a speed of \( 34 \) \( \text{m/s} \). What is the ball’s final speed when it hits the ground below?

Beginner
Conceptual
MCQ

You drive \( 4 \) \( \text{km} \) at \( 30 \) \( \text{km/h} \) and then another \( 4 \) \( \text{km} \) at \( 50 \) \( \text{km/h} \). What is your average speed for the whole \( 8 \) \( \text{km} \) trip?

Intermediate
Mathematical
MCQ

An object of mass 2 kg is thrown vertically downwards with an initial kinetic energy of 100 J. What is the distance fallen by the object at the instant when its kinetic energy has doubled?

Advanced
Proportional Analysis
MCQ

Two identical object rests on a platform rotating at constant speed. Object A is at distance of half the platform’s radius from the center. Object B lays at edge of the platform. Assuming the platform continues rotating at the same speed, how does the centripetal force of the two objects compare?

Advanced
Mathematical
GQ

A \(3300 \, \text{m}\)-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The Earth’s radius is \(6400 \, \text{km}\) and the Earth’s mass is \(5.97 \times 10^{24} \, \text{kg}\).

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

An object moves at a constant speed of \( 9.0 \frac{m}{s} \) in a circular path of radius of 1.5 m. What is the angular acceleration of the object?

Beginner
Mathematical
GQ

Two students start \( 100 \) \( \text{m} \) apart.

• Student A walks to the right at \( 2 \) \( \text{m/s} \).

• Student B walks to the left at \( 3 \) \( \text{m/s} \).

At what time do the students meet, and how far has each student walked when they collide?

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