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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?

Beginner
Conceptual
MCQ

Which launch angle gives the greatest horizontal range, assuming level ground and no air resistance?

Beginner
Mathematical
GQ

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

Intermediate
Mathematical
FRQ

A spacecraft accelerates at a rate of \(20.0 \, \text{m/s}^2\).

Advanced
Conceptual
MCQ
Figure 1. A uniform hoop of radius R rolling without slipping on a horizontal surface.
Figure 1. A uniform hoop of radius R rolling without slipping on a horizontal surface.

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?

Beginner
Mathematical
MCQ

A block is attached to a horizontal spring. The block is held so the spring is stretched and the block is released from rest, undergoing simple harmonic motion with a frequency of \( 2 \) \( \text{Hz} \). How long after release will the block first reach a point where it is momentarily at rest?

Intermediate
Mathematical
GQ

A truck is traveling at \(35 \, \text{m/s}\) when the driver realizes the truck has no brakes. He sees a ramp off the road, inclined at \(20^\circ\), and decides to go up it to help the truck come to a stop. How far does the truck travel before coming to a stop (assume no friction)?

Advanced
Mathematical
GQ

A \(1 \, \text{kg}\) mass and an unknown mass \(M\) hang on opposite sides of a pulley suspended from the ceiling. When the masses are released, \(M\) accelerates downward at \(5 \, \text{m/s}^2\). Find the value of \(M\).

Intermediate
Conceptual
MCQ

An isolated spherical star of radius \( R_o \), rotates about an axis that passes through its center with an angular velocity of \( \omega_o \). Gravitational forces within the star cause the star’s radius to collapse and decrease to a value \( r_o < R_o \), but the mass of the star remains constant. A graph of the star’s angular velocity as a function of time as it collapses is shown. Which of the following predictions is correct about the angular momentum \( L \) of the star immediately after the collapse?

Advanced
Mathematical
FRQ

A particle of mass \(m\) slides down a fixed, frictionless sphere of radius \(R\), starting from rest at the top.

In terms of \(m\), \(g\), \(R\), and \(\theta\), determine each of the following for the particle while it is sliding on the sphere.

Intermediate
Mathematical
FRQ

Measurements made in 1910 indicate that the common flea is an impressive jumper, given its size. Assume that a flea’s initial speed is 2.1 m/s, and that it leaps at an angle of 21° with respect to the horizontal. The jump lasts 0.16 s.

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