You are told that a basketball player spins the ball with an angular acceleration of 100 rad/s$^2$. (a) What is the ball's final angular velocity if the ball starts from rest and the acceleration lasts 2.00 s? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

A basketball player drops a $0.60-k g$ basketball vertically so that it is traveling at $6.0 \mathrm{m} / \mathrm{s}$ when it reaches the floor. The ball rebounds upwardat a speed of $4.2 \mathrm{m} / \mathrm{s}$. (a) Determine the magnitude and direction of the ball’s change in momentum. (b) Determine the average net force that the floor exerts on the ball if the collision lasts $0.12 \mathrm{s}$.

A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from $18.5$ to $14.1 \mathrm{rad} / \mathrm{s}$. During the slow-down, the angular displacement is $85.1 \mathrm{rad}$. Determine the time it takes for the ball to slow down.

You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone. (b) How many turns will the stone make before coming to rest?

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 18.5 to 14.1 rad/s. During the slow-down, the angular displacement is 85.1 rad. Determine the time it takes for the ball to slow down.

Determine the value for k that will make the function continuous at c = 4.

$$f(x)=\left\{\begin{array}{ll}{\frac{x^{2}-9}{x+3}} & {\text { if } x \leq 4} \\ {k x+5} & {\text { if } x>4}\end{array}\right.$$

Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?

Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. a. What is its angular acceleration in rad/s²? b.What is the tangential acceleration (in m/s²) of a point 10.00 cm from the axis of rotation? c. What is the radial acceleration in m/s²? and in multiples of g of this point at full rpm?

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

Consider the function $f(x)=\frac{e^{x}}{x-1}$. Find the equation of the tangent at the point where x = 2.

How might deforestation lead to desertification?

A 32.5-g iron rod, initially at 22.7 $^{\circ} \mathrm{C}$, is submerged into an unknown mass of water at 63.2$^{\circ} \mathrm{C}$, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 59.5$^{\circ} \mathrm{C}$. What is the mass of the water?