A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 $k g \cdot m ^ { 2 }$ is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

An object of mass 2.00 kg is oscillating freely on a vertical spring with a period of 0.600 s. Another object of unknown mass on the same spring oscillates with a period of 1.05 s. Find the unknown mass.

What three variables influence the speed of stream flow?

Describe two advantages of using credit cards.

The area of an oil spill is increasing at a rate of 25t

$$\mathrm { ft } ^ { 2 } / \mathrm { s }$$

seconds after the spill. Between times t=2 and t=4 the area of the spill increases by ___

$$ft^2$$

.

A model airplane with mass 0.750 kg is tethered by a wire so that it flies in a circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendicular to the tethering wire. Find the linear acceleration of the airplane tangent to its flight path.

A model airplane with mass 0.750 kg is tethered by a wire so that it flies in a circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendicular to the tethering wire. Find the angular acceleration of the airplane when it is in level flight.

A rope of negligible mass is wrapped around a 225-kg solid cylinder of radius 0.400 m. The cylinder is suspended several meters off the ground with its axis oriented horizontally, and turns on that axis without friction. If the mass of the rope were not neglected, what would happen to the angular acceleration of the cylinder as the man falls?

A potter is shaping a bowl on a potter's wheel rotating at constant angular speed. The friction force between her hands and the clay is 1.5 N total. How long would it take for the potter's wheel to stop if the only torque acting on it is due to the potter's hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is $0.11 \mathrm{kg} \cdot \mathrm{m}^{2}$.

Sketch the curves of the given functions by addition of ordinates. $y=3-2 \cos x$

A model airplane with mass 0.750 kg is tethered to the ground by a wire so that it flies in a horizontal circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendicular to the tethering wire. (a) Find the torque the net thrust produces about the center of the circle. (b) Find the angular acceleration of the airplane. (c) Find the translational acceleration of the airplane tangent to its flight path.

A rope of negligible mass is wrapped around a 225-kg solid cylinder of radius 0.400 m. The cylinder is suspended several meters off the ground with its axis oriented horizontally, and turns on that axis without friction. If a 75.0-kg man takes hold of the free end of the rope and falls under the force of gravity, what is his acceleration?

Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.

$$\begin{gather*} (x + 3)y'' + xy' + (\ln |x|)y = 0, \,\,\, y(1) = 0, \,\,\, y'(1) = 1 \end{gather*}$$

The wheel of a car has a radius of 0.350 m. The engine of the car applies a torque of $295 \mathrm{N} \cdot \mathrm{m}$ to this wheel , which does not slip against the road surface . Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a counter-torque. Moreover, the car has a constant velocity , so this counter-torque balances the applied torque . What is the magnitude of the static frictional force?