Suppose that the Sun runs out of nuclear fuel and suddenly collapses to form a so-called white dwarf star, with a diameter equal to that of the Earth. Assuming no mass loss, what would then be the new rotation period of the Sun, which cur- rently is about $25$ days? Assume that the Sun and the white dwarf are uniform spheres.

A uniform rod rotates in a horizontal plane about a vertical axis through one end. The rod is 6.00 meters long, weighs 10.0 Newtons, and rotates at $240 \text{~rev/min}$. Calculate its rotational inertia about the axis of rotation.

Thermal pollution has a harmful effect on aquatic environments because a. water has been circulated around power-plant generators. b. it increases the number of disease-causing organisms in aquatic environments. c. it reduces the amount of dissolved oxygen in aquatic environments. d. it decreases the nutrient levels in aquatic environments.

Choose the letter of the best answer. Which of the following is an example of a point source of water pollution? F runoff of pesticides from wheat fields G salt spread on parking lots to melt ice H chemicals flowing from a factory into a stream J fertilizer from corn fields that runs off into streams

Pollution from which of the following is an example of point source pollution? a. Fertilizers from agricultural fields b. Runoff from Midwestern farms c. Oil spills from leaky pipelines d. Pesticides from farmlands e. Smoke from an industrial plant smokestack

A frigate bird is soaring in a horizontal circular path. Its bank angle is estimated to be $25\degree$ and it takes $13$ s for the bird to complete one circle. $(a)$ How fast is the bird flying? $(b)$ What is the radius of the circle? (See “The Amateur Scientist” by Jearl Walker, $\it{Scientific~ American}$, March $1985$, p. $122$.)

A worker drags a $150$-lb crate across a floor by pulling on a rope inclined $17\degree$ above the horizontal. The coefficient of sta- tic friction is $0.52$ and the coefficient of kinetic friction is $0.35$. $(a)$ What tension in the rope is required to start the crate moving? $(b)$ What is the initial acceleration of the crate?

Astronomical observations show that from $1870$ to $1900$ the length of the day increased by about $6.0 \times 10^{-3}$ s. $(a)$ What corresponding fractional change in the Earth’s angular veloc- ity resulted? $(b)$ Suppose that the cause of this change was a shift of molten material in the Earth’s core. What resulting fractional change in the Earth’s rotational inertia could ac- count for the answer to part $(a)$?

A piece of ice slides from rest down a rough $33.0\degree$ incline in twice the time it takes to slide down a frictionless $33.0\degree$ in- cline of the same length. Find the coefficient of kinetic fric- tion between the ice and the rough incline.

Frictional heat generated by the moving ski is the chief factor promoting sliding in skiing. The ski sticks at the start, but once in motion will melt the snow beneath it. Waxing the ski makes it water repellent and reduces friction with the film of water. A magazine reports that a new type of plastic ski is even more water repellent and that, on a gentle $203$-m slope in the Alps, a skier reduced his time from $61$ to $42$ s with the new skis. Assuming a $3.0\degree$ slope, compute the coefficient of kinetic friction for each case.

A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.4 m/s². (a) If the tension in the cord is 89 N, what is the lamp’s mass? (b) What is the cord’s tension when the elevator ascends with an upward acceleration of 2.4 m/s²?

A helicopter flies off, its propellers rotating. Why doesn’t the body of the helicopter rotate in the opposite direction?

A cylinder rolls down an inclined plane of angle $\theta$. Show, by direct application of earlier Eq. $(\Sigma \overrightarrow{\boldsymbol{\tau}}_{\text {ext }}=d \overrightarrow{\mathbf{L}} / d t)$ that the accel- eration of its center of mass is $\frac{2}{3} g \sin \theta$. Compare this method with that used in earlier Sample Problem.

A uniform stick has a mass of $4.42$ kg and a length of $1.23$ m. It is initially lying flat at rest on a frictionless horizontal sur- face and is struck perpendicularly by a puck imparting a hori- zontal impulsive force of impulse $12.8$ $\mathrm{N}~ \cdot$ s at a distance of $46.4$ cm from the center. Determine the subsequent motion of the stick.