Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(d)$ Which point has the greater angular speed?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(f)$ Which point has the greater angular acceleration?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(c)$ Which point has the greater speed?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(b)$ Which point turns through the greater angle?

Two points are on a disk that rotates about an axis perpendicular to the plane of the disk at its center. Point $B$ is 3 times as far from the axis as point $A$. If the linear speed of point $B$ is $V$, then the linear speed of point $A$ is
A. $9 \mathrm{~V}$
B. $3 \mathrm{~V}$
C. V
D. $\frac{V}{3}$.
E. $\frac{V}{9}$.

Romeo takes a uniform $10\text{-m}$ ladder and leans it against the smooth (frictionless) wall of the Capulet residence. The ladder's mass is $22 \mathrm{~kg}$ and the bottom rests on the ground $2.8 \mathrm{~m}$ from the wall. When Romeo, whose mass is $70 \mathrm{~kg}$, gets $90$ percent of the way to the top, the ladder begins to slip. What is the coefficient of static friction between the ground and the ladder?

A $100\text{-kg}$ spacecraft is in a circular orbit about Earth at a height $h=2 R_{\text{E}}$. $(c)$ Express the angular momentum $L$ of the spacecraft about the center of Earth in terms of the kinetic energy $K$ and find the numerical value of $L$.

A $100\text{-kg}$ spacecraft is in a circular orbit about Earth at a height $h=2 R_{\text{E}}$. $(b)$ What is the spacecraft's kinetic energy?

A $100\text{-kg}$ spacecraft is in a circular orbit about Earth at a height $h=2 R_{\text{E}}$. $(a)$ What is the orbital period of the spacecraft?

A particle is projected from the surface of Earth with a speed twice the escape speed. When it is very far from Earth, what is its speed?

An object is dropped from rest from a height of $4.0 \times 10^6 \text{~m}$ above the surface of Earth. If there is no air resistance, what is its speed when it strikes Earth?

An object is projected straight upward from the surface of Earth with an initial speed of $4.0 \text{~km/s}$. What is the maximum height it reaches?

Two ice-skaters, whose masses are $55 \mathrm{~kg}$ and $85 \mathrm{~kg}$, hold hands and rotate about a vertical axis that passes between them, making one revolution in $2.5 \mathrm{~s}$. Their centers of mass are separated by $1.7 \mathrm{~m}$, and their center of mass is stationary. Model each skater as a point particle and find

$(b)$ the total kinetic energy of the system.

Two ice-skaters, whose masses are $55 \mathrm{~kg}$ and $85 \mathrm{~kg}$, hold hands and rotate about a vertical axis that passes between them, making one revolution in $2.5 \mathrm{~s}$. Their centers of mass are separated by $1.7 \mathrm{~m}$, and their center of mass is stationary. Model each skater as a point particle and find

$(a)$ the angular momentum of the system about their center of mass.