A solid uniform cylinder with mass $8.25 \mathrm{~kg}$ and diameter $15.0 \mathrm{~cm}$ is spinning at $220 \mathrm{~rpm}$ on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is $0.333$. What must the applied normal force be to bring the cylinder to rest after it has turned through $5.25$ revolutions?

A certain type of propeller blade can be modeled as a thin uniform bar $2.50 \mathrm{~m}$ long and of mass $24.0 \mathrm{~kg}$ that is free to rotate about a frictionless axle perpendicular to the bar at its midpoint. If a technician strikes this blade with a mallet $1.15 \mathrm{~m}$ from the center with a $35.0 \mathrm{~N}$ force perpendicular to the blade, find the maximum angular acceleration the blade could achieve.

The propeller of a light plane has a length of $2.092 \mathrm{~m}$ and a mass of $17.56 \mathrm{~kg}$. The rotational energy of the propeller is $422.8 \mathrm{~kJ}$. What is the rotational frequency of the propeller (in rpm)? You can treat the propeller as a thin rod rotating about its center.

A uniform beams $4.0 \mathrm{~m}$ long and weighing $2500 \mathrm{~N}$ carries a $3500 \mathrm{~N}$ weight $1.50 \mathrm{~m}$ from the far end. It is supported horizontally by a hinge at the wall and a metal wire at the far end.
(a) Make a free-body diagram of the beam.
(b) How strong does the wire have. to be? That is, what is the minimum tension it must be able to support without breaking?
(c) What are the horizontal and vertical components of the force that the hinge exerts on the beam?

A large wooden turntable in the shape of a flat disk has a radius of $2.00 \mathrm{~m}$ and a total mass of $120 \mathrm{~kg}$. The turntable is initially rotating at $3.00 \mathrm{rad} / \mathrm{s}$ about a vertical axis through its center. Suddenly, a $70.0 \mathrm{~kg}$ parachutist makes a soft landing on the turntable at a point on its outer edge. Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.)

A 7.4 cm diameter baseball has mass 145 g and is spinning at 2000 rpm. Treating the baseball as a uniform solid sphere, what's its angular momentum?

Three forces are applied to a wheel of radius 0.350, as shown in the figure (Intro 1figure). One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.0 angle with the radius. Assume that $F_1=12.4~\text{N}$, $F_2=14.2~\text{N}$, and $F_3=8.75~\text{N}$.

Part A What is the magnitude of the net torque on the wheel due to these three forces for an axis perpendicular to the wheel and passing through its center?

Part B What is the direction of the net torque in part (A), into the page or out of the page?

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center. When the skater's hand and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled, hollow cylinder. His hans and arms have a combined mass of 8.0 kg. When outstretched, they span 1.8 m; when wrapped, they form a cylinder of radius 25 cm. The moment of inertia about the rotation of the remainder of his body is constant and equal to 0.40 kg $\cdot$ m$^2$. If his original angular speed is 0.40 rev/s, what is his final angular speed?

Two people are carrying a uniform wooden board that is $3.00 {m}$ long and weighs $160 \mathrm{~N}$. If one person applies an upward force equal to $60 \mathrm{~N}$ at one end, at what point does the other person lift? Begin with a free-body diagram of the board.

Calculate the torque (magnitude and direction) about point O due to the force $\vec{F}$ in each of the cases sketched in the given figure. The force $\vec{F}$ and the rod both lie in the plane of the page, the rod has length $4.00 \mathrm{~m}$, and the force has magnitude $F=10.0 \mathrm{~N}$. Angle F with horizontal is 0$^\circ$.

Calculate the torque (magnitude and direction) about point O due to the force $\vec{F}$ in each of the cases sketched in the given figure. The force $\vec{F}$ and the rod both lie in the plane of the page, the rod has length $4.00 \mathrm{~m}$, and the force has magnitude $F=10.0 \mathrm{~N}$. The angle between O and F is $0^\circ$.

Calculate the torque (magnitude and direction) about point O due to the force $\vec{F}$ in each of the cases sketched in the given figure. The force $\vec{F}$ and the rod both lie in the plane of the page, the rod has length $4.00 \mathrm{~m}$, and the force has magnitude $F=10.0 \mathrm{~N}$. The angle between O and F is $90^\circ$.

A uniform metal meterstick is balanced with a $1.0 \mathrm{~kg}$ rock attached to the left end of the stick. What is the mass of the meterstick?
A. $0.60 \mathrm{~kg}$.
B. $1.0 \mathrm{~kg}$.
C. $2.0 \mathrm{~kg}$.
D. $3.0 \mathrm{~kg}$.

A student is sitting on a frictionless rotating stool with her arms outstretched holding equal heavy weights in each hand. If she suddenly lets go of the weights, her angular speed will
A. increase
B. stay the same
C. decrease.