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Intermediate
Mathematical
GQ

An object moves at constant speed in a circular path of radius \( r \) at a rate of \( 1 \) revolution per second. What is its acceleration in terms of \(r\)?

Beginner
Conceptual
GQ

According to Newton’s third law, each team in a tug of war pulls with equal force on the other team. What, then, determines which team will win?

Intermediate
Conceptual
GQ

You throw a ball straight upward. It leaves your hand at \( 20 \) \( \text{m/s} \) and slows at a steady rate until it stops at the peak. The ball then comes back down, speeding up steadily until it hits the ground with the same speed it left your hand. Draw the velocity vs. time graph or explain it in terms of functions.

Intermediate
Conceptual
MCQ

Two identical metal balls are being held side by side at the top of a ramp. Alex lets one ball, \( A \), start rolling down the hill. A few seconds later, Alex’s partner, Bob, starts the second ball, \( B \), down the hill by giving it a push. Ball \( B \) rolls down the hill along a line parallel to the path of the first ball and passes it. At the instant ball \( B \) passes ball \( A \):

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?

Advanced
Mathematical
GQ

The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. Suppose a scientist makes a slight error in sample preparation and one sample has a mass \( 10 \) \( \text{mg} \) larger than the opposing sample.

 

If the samples are \( 12 \) \( \text{cm} \) from the axis of the rotor and the ultracentrifuge spins at \( 60000 \) \( \text{rpm} \), what is the magnitude of the net force on the rotor due to the unbalanced samples?

Beginner
Conceptual
MCQ

A block rests on a frictionless incline. Which statement is correct?

Beginner
Conceptual
MCQ

When a box is about to slide but hasn’t moved yet, which friction is acting?

Advanced
Mathematical
MCQ

In a lab experiment, a ball is rolled down a ramp so that it leaves the edge of the table with a horizontal velocity [katex]v[/katex]. Assume there are no frictional forces. If the table has a height [katex]h[/katex] above the ground, how far away from the edge of the table, a distance [katex]x[/katex], does the ball land?

Beginner
Mathematical
MCQ

A turntable rotates through \( 6 \) \( \text{rad} \) in \( 3 \) \( \text{s} \) as it accelerates uniformly from rest. What is its angular acceleration in \( \text{rad/s}^2 \)?

Intermediate
Mathematical
GQ

At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull in opposite directions with equal force?

Beginner
Mathematical
GQ

A rotating, rigid body makes 10 complete revolutions in 10 seconds. What is its average angular velocity?

Beginner
Mathematical
GQ

A disk of radius 35 cm rotates at a constant angular velocity of 10 rad/s. How fast does a point on the rim of the disk travel (in m/s)?

Advanced
Mathematical
FRQ

An eagle is flying horizontally at \(6 \, \text{m/s}\) with a fish in its claws. It accidentally drops the fish.

Advanced
Conceptual
MCQ

When the speed of a rear-wheel-drive car is increasing on a horizontal road, what is the direction of the frictional force on the tires?

Advanced
Mathematical
MCQ

A ball of mass \( m \) is suspended from two strings of unequal length as shown above. The magnitudes of the tensions \( T_1 \) and \( T_2 \) in the strings must satisfy which of the following relations?

 

Intermediate
Mathematical
MCQ

A mechanical wheel initially at rest on the floor begins rolling forward with an angular acceleration of \( 2\pi \, \text{rad/s}^2 \). If the wheel has a radius of \( 2 \, \text{m} \), what distance does the wheel travel in \( 3 \) seconds?

Intermediate
Mathematical
GQ

Determine the force needed to push a \( 150 \) \( \text{kg} \) body up a smooth \( 30^\circ \) incline with an acceleration of \( 6 \) \( \text{m/s}^2 \).

Intermediate
Mathematical
MCQ

A \(0.10 \, \text{kg}\) ball, traveling horizontally at \(25 \, \text{m/s}\), strikes a wall and rebounds at \(19 \, \text{m/s}\). What is the magnitude of the change in the momentum of the ball during the rebound?

Advanced
Conceptual
FRQ

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with \( \theta_A \) larger than \( \theta_B \).

Beginner
Mathematical
GQ

A spring with a spring constant of \( 600. \) \( \text{N/m} \) is used for a scale to weigh fish. What is the mass of a fish that would stretch the spring by \( 7.5 \) \( \text{cm} \) from its normal length?

Advanced
Mathematical
MCQ

A construction worker spins a square sheet of metal of mass 0.040 kg with an angular acceleration of 10.0 rad/s2 on a vertical spindle (pin). What are the dimensions of the sheet if the net torque on the sheet is 1.00 N·m? Assume that the moment of inertia of a rectangle is [katex] I = \frac{1}{12}M(a^2+b^2) [/katex]

Beginner
Proportional Analysis
MCQ

Jill does twice as much work as Jack does and in half the time. Jill’s power output is

Intermediate
Mathematical
GQ

A bald eagle in level flight at a height of \(135 \, \text{m}\) drops the fish it caught. If the eagle’s speed is \(25.0 \, \text{m/s}\) how far from the drop point will the fish land?

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