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Advanced
Mathematical
MCQ

A block attached to spring demonstrates simple harmonic motion about its equilibrium position with amplitude \( A \) and angular frequency \( \omega \). What is the maximum magnitude of the block’s velocity?

Intermediate
Conceptual
MCQ

One end of a string is wrapped around a pulley that is free to rotate with negligible friction about an axle at its center. The other end of the string is attached to a block. The block is released from rest and moves downward with constant acceleration. Which of the following correctly indicates whether the amount of work done on the pulley by the string during each successive complete rotation remains constant or increases, and provides a valid justification?

Advanced
Proportional Analysis
MCQ

A rock is whirled on the end of a string in a horizontal circle of radius \(R\) with a constant period \(T\). If the radius of the circle is reduced to \(R/3\), while the period remains \(T\), what happens to the centripetal acceleration (\(a_c\)) of the rock?

Advanced
Mathematical
GQ

A horizontal uniform meter stick of mass 0.2 kg is supported at its midpoint by a pivot point. A mass of 0.1 kg is attached to the left end of the meter stick, and another mass of 0.15 kg is attached to the right end of the meter stick. The meter stick is free to rotate in the horizontal plane around the pivot point. What is the tension in the string supporting the left end of the meter stick?

Intermediate
Mathematical
FRQ

Young David experimented with slings before tackling Goliath. He found that he could develop an angular speed of \( 8.0 \) \( \text{rev/s} \) in a sling \( 0.60 \) \( \text{m} \) long. If he increased the length to \( 0.90 \) \( \text{m} \), he could revolve the sling only \( 6.0 \) times per second.

Beginner
Conceptual
MCQ

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

Intermediate
Mathematical
FRQ

A geologist suspects that her rock specimen is hollow, so she weighs the specimen in both air and water. When completely submerged, the rock weighs twice as much in air as it does in water.

Beginner
Conceptual
GQ

A car moves forward at a steady \( 10 \) \( \text{m/s} \) for \( 5 \) \( \text{s} \). The driver slams the brakes and brings it to rest in \( 2 \) \( \text{s} \). Without waiting, the driver immediately accelerates backward (negative velocity) for \( 3 \) \( \text{s} \) until reaching \( 8 \) \( \text{m/s} \) in reverse. Draw the velocity vs. time graph.

Advanced
Mathematical
FRQ

A snowboarder starts from rest and slides down a \(32^\circ\) incline that’s \(75 \, \text{m}\) long.

Intermediate
Mathematical
FRQ

A textbook is launched up with a speed of 20 m/s, at an angle of 36°, from a 12 m high roof.

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
GQ

A golfer hits a shot to a green that is elevated \(2.80 \, \text{m}\) above the point where the ball is struck. The ball leaves the club at a speed of \(18.9 \, \text{m/s}\) at an angle of \(52.0^\circ\) above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.

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.

Beginner
Conceptual
MCQ

A light string is attached to a massive pulley of known rotational inertia \( I_P \), as shown in the figure. A student must determine the relationship between the torque exerted on the pulley and the change in the pulley’s angular velocity when the torque is applied for \( 2.0 \) \( \text{s} \). In addition to a stopwatch to measure the time interval, what two measurements could the student make in order to determine the relationship? Select two answers.

Intermediate
Mathematical
GQ

Barry Bonds hits a \(125 \,\text{m}\) home run. Assuming that the ball left the bat at an angle of \(45^\circ\) from the horizontal, calculate how long the ball was in the air.

Intermediate
Mathematical
MCQ

A wheel of moment of inertia of \( 5.00 \) \( \text{kg} \cdot \text{m}^2 \) starts from rest and accelerates under a constant torque of \( 3.00 \) \( \text{N} \cdot \text{m} \) for \( 8.0 \) \( \text{s} \). What is the wheel’s rotational kinetic energy at the end of \( 8.0 \) \( \text{s} \)?

Intermediate
Mathematical
GQ

On a strange, airless planet, a ball is thrown downward from a height of \( 17 \, \text{m} \). The ball initially travels at \( 15 \, \text{m/s} \). If the ball hits the ground in \( 1 \, \text{s} \), what is this planet’s gravitational acceleration?

Advanced
Mathematical
FRQ

Refer to the diagram above and solve all equations in terms of \(R\), \(M\), \(k\), and constants.

Intermediate
Conceptual
GQ

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

Beginner
Conceptual
MCQ

During projectile motion (neglecting air resistance), what is the vertical acceleration at the highest point, assuming the initial velocity is upwards in the positive direction?

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

Intermediate
Mathematical
GQ

A wheel 31 cm in diameter accelerates uniformly from 240rpm to 360rpm in 6.8 s. How far will a point on the edge of the wheel have traveled in this time?

Beginner
Mathematical
GQ

A car starts from rest and accelerates uniformly over a time of 5 seconds for a distance of 100 m. Determine the acceleration of the car.

Intermediate
Conceptual
MCQ

In which of the following is the rate of change of the particle’s momentum zero?

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