Parallel Parking
This equation, I = Icm + Md², allows you to find the moment of inertia about any axis parallel to one through the center of mass.
What is the Parallel-Axis Theorem?
In projectile motion, this remains constant throughout the entire flight (neglecting air resistance).
What is horizontal velocity (or horizontal component of velocity)?
This is the rotational analog of mass in Newton's second law for rotation.
What is rotational inertia?
This quantity is the rotational analog of velocity and is measured in radians per second.
What is angular velocity (ω)?
On a position vs. time graph, this quantity is represented by the slope of the line.
What is velocity?
The Parallel-Axis Theorem only works when the two axes have this specific orientation relative to each other.
What is parallel?
A ball is launched horizontally from a 20 m high cliff with an initial speed of 10 m/s. This is the time it takes to hit the ground.
What is 2 seconds?
A force of 20 N is applied perpendicular to a door 0.8 m from the hinges. This is the magnitude of the torque about the hinges.
What is 16 N⋅m?
A wheel rotating at 20 rad/s undergoes constant angular acceleration of -4 rad/s² for 3 seconds. This is its final angular velocity.
What is 8 rad/s?
A velocity vs. time graph shows a horizontal line above the time axis. This type of motion is being represented.
What is constant velocity motion (or uniform motion)?
A uniform rod has a moment of inertia of ML²/12 about its center. Using the Parallel-Axis Theorem, what is its moment of inertia about one end?
What is ML²/3?
For a projectile launched at an angle above the horizontal, the velocity has this value at the highest point of its trajectory.
What is the horizontal component of the initial velocity (v₀ cos θ)?
When the same torque is applied to two objects, the one with smaller rotational inertia will have this type of angular acceleration.
What is larger (or greater)?
For a point on a rotating wheel at distance r from the axis, the linear speed v is related to angular speed ω by this equation.
What is v = rω?
On a velocity vs. time graph, the area under the curve represents this quantity.
What is displacement (or change in position)?
A thin hoop of mass 2.0 kg and radius 0.5 m has I_cm = MR² about its center. What is its moment of inertia about a point on its rim?
What is 1.0 kg⋅m²?
A projectile is launched at 30° above horizontal with initial speed v₀. At the highest point, the ratio of kinetic energy to initial kinetic energy is this value.
What is 3/4?
A disk and a ring of equal mass and radius roll down the same incline. This object reaches the bottom first.
What is the disk?
A merry-go-round accelerates from rest with constant angular acceleration of 0.5 rad/s². This is the angle (in radians) it rotates through in the first 4 seconds.
What is 4 radians?
An object's position vs. time graph is a parabola opening upward. The slope of the velocity vs. time graph for this motion has this characteristic.
What is positive (or constant and positive)?
A solid sphere of mass M and radius R rolls without slipping down an incline. If its moment of inertia about its center is 2MR²/5, what is its moment of inertia about the instantaneous point of contact with the ground?
What is 7MR²/5?
Two projectiles are launched from the same height with the same initial speed. One at 30° above horizontal, the other at 60°. This is the ratio of their ranges.
What is 1?
A figure skater spins with arms extended at 2 rad/s. When she pulls her arms in, reducing her rotational inertia by half, her new angular velocity is this value.
What is 4 rad/s?
A wheel of radius 0.3 m rolls without slipping. When it completes 10 full rotations, the linear distance traveled by its center is this value.
What is 18.85 meters?
Force is plotted vs. position for a spring. To find the spring constant from this graph, you must determine this feature of the graph.
What is the slope?