A wheel rotates with a constant angular velocity of $6.00 \mathrm{rad} / \mathrm{s}$. a) Compute the radial acceleration of a point $0.500 \mathrm{~m}$ from the axis, using the relation $a_{\text {tad }}=\omega^2 r$. b) Find the tangential speed of the point and compute its radial acceleration from the relation $a_{\mathrm{rad}}=\frac{v^2}{ r}$

A car is traveling at a speed of $63 \mathrm{mi} / \mathrm{h}$ on a freeway. If its tires have a diameter of $24.0$ and are rolling without sliding or slipping, what is their angular velocity?

A turntable rotates with a constant $2.25 \mathrm { rad } / \mathrm { s } ^ { 2 }$ angular acceleration. After 4.00 s it has rotated through an angle of 30.0 rad. What was the angular velocity of the wheel at the beginning of the 4.00-s interval?

A flywheel having constant angular acceleration requires $4.00 \mathrm{~s}$ to rotate through $162 \mathrm{rad}$. Its angular velocity at the end of this time is $108 \mathrm{rad} / \mathrm{s}$. Find
(a) the angular velocity at the beginning of the $4.00 \mathrm{~s}$ interval;
(b) the angular acceleration of the flywheel.

A circular saw blade $0.200 \textrm{ m}$ in diameter starts from rest. In $6.00 \textrm{ s}$ it accelerates with constant angular acceleration to an angular velocity of $140 \textrm{ rad/s}$. Find the angular acceleration and the angle through which the blade has turned.

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0 cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0-kg person, the mass of the upper leg would be 8.60 kg, while that of the lower leg (including the foot) would be 5.25 kg. Find the location of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of $0.600 \mathrm { rad } / \mathrm { s } ^ { 2 }$. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start.

A $60 \mathrm{~kg}$ woman steps onto an up-going escalator, which has an incline of $32^{\circ}$ with respect to the horizontal and is moving at $0.5 \mathrm{~m} / \mathrm{s}$. The top of the escalator is $20 \mathrm{~m}$ above the ground level. Calculate how much work is done by
(a) the friction force between the woman's feet and the escalator step,\ (b) gravity, and
(c) the normal force on the woman's feet, as she moves from the bottom to the top of the escalator. What is the total work done on the woman as she moves from the bottom to the top?

A 52-kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched; she makes 2.0 turns each second. The distance from one hand to the other is 1.50 m. Biometric measurements indicate that each hand typically makes up about 1.25% of body weight. (a) Draw a free-body diagram of one of the skater’s hands. (b) What horizontal force must her wrist exert on her hand? (c) Express the force in part (b) as a multiple of the weight of her hand.

A compact disc (CD) stores music in a coded pattern of tiny pits $10^{-7}$ m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are $25.0$ mm and $58.0$ mm, respectively. As the dise spins inside a CD player, the track is scanned at a constant $\it{linear}$ speed of $1.25$ m$/$s.
($c$) What is the average angular acceleration of a maximum- duration CD during its $74.0$-min playing time? Take the direction of rotation of the disc to be positive.

A compact disc (CD) stores music in a coded pattern of tiny pits $10^{-7}$ m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are $25.0$ mm and $58.0$ mm, respectively. As the dise spins inside a CD player, the track is scanned at a constant $\it{linear}$ speed of $1.25$ m$/$s.
(b) The maximum playing time of a $\mathrm{CD}$ is $74.0$ min. What would be the length of the track on such a maximum-duration $\mathrm{CD}$ if it were stretched out in a straight line?

A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point $A$ is on the rim of the wheel and point $B$ is midway between the rim and center of the wheel. For each of the following quantities, is its magnitude larger at point $A$ or at point $B$, or is it the same at both points? angular acceleration;

The main rotor of a helicopter is turning in a horizontal plane at $90.0 \mathrm{rev} / \mathrm{min}$. The distance from the center of the rotor shaft to each blade tip is $5.00 \mathrm{~m}$. Calculate the speed through the air of the blade tip if a) the helicopter is sitting on the ground; b) the helicopter is rising vertically at $4.00 \mathrm{~m} / \mathrm{s}$.

A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point $A$ is on the rim of the wheel and point $B$ is midway between the rim and center of the wheel. For each of the following quantities, is its magnitude larger at point $A$ or at point $B$, or is it the same at both points? tangential speed;