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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?

Advanced
Mathematical
FRQ

A \(20 \, \text{g}\) piece of clay moving at a speed of \(50 \, \text{m/s}\) strikes a \(500 \, \text{g}\) pendulum bob at rest. The length of a string is \(0.8 \, \text{m}\). After the collision, the clay-bob system starts to oscillate as a simple pendulum.

Beginner
Conceptual
GQ

Two students hold a large bed sheet vertically between them. A third student, who happens to be the star pitcher on the school baseball team, throws a raw egg at the center of the sheet. Explain why the egg does not break when it hits the sheet, regardless of its initial speed.

Intermediate
Mathematical
MCQ

A uniform stick has length \( L \). The moment of inertia about the center of the stick is \( I_0 \). A particle of mass \( M \) is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is

Beginner
Mathematical
GQ

A car accelerates from rest with an acceleration of \( 4.3 \, \text{m/s}^2 \) for a time of \( 6.8 \, \text{s} \). The car then slows to a stop with an acceleration of \( 5.1 \, \text{m/s}^2 \). What is the total distance traveled by the car?

Intermediate
Mathematical
GQ

A communications satellite orbits the Earth at an altitude of \(35{,}000 \, \text{km}\) above the Earth’s surface. Take the mass of Earth to be \(6 \times 10^{24} \, \text{kg}\) and the radius of Earth to be \(6.4 \times 10^6 \, \text{m}\). What is the satellite’s velocity?

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?

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?

Intermediate
Mathematical
MCQ

A linear spring of force constant \( k \) is used in a physics lab experiment. A block of mass \( m \) is attached to the spring and the resulting frequency, \( f \), of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If \( f^{2} \) is plotted versus \( \frac{1}{m} \), the graph will be a straight line with slope

Intermediate
Mathematical
FRQ

Two racing boats set out from the same dock and speed away at the same constant speed of \(101 \, \text{km/h}\) for half an hour (\(0.5 \, \text{hr}\)). Boat 1 is headed \(27.6^\circ\) south of west, and Boat 2 is headed \(35.3^\circ\) south of west, as shown in the graph above. During this half-hour calculate:

Beginner
Conceptual
MCQ

The magnitude of a component of a vector must be

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