Chapter 9

Find each missing quantity using \(D \cdot N=d \cdot n\). $$ \begin{array}{cccc} D & N & d & n \\ \hline 18.0 & 1500 & 12.0 & \end{array} $$

Convert \(6 \frac{1}{2}\) revolutions (a) to radians. (b) to degrees.

Find each missing quantity using \(D \cdot N=d \cdot n\). $$ \begin{array}{cccc} D & N & d & n \\ \hline 36.0 & & 9.00 & 972 \end{array} $$

Convert \(2880^{\circ}\) (a) to revolutions. (b) to radians.

Find each missing quantity using \(D \cdot N=d \cdot n\). $$ \begin{array}{cccc} D & N & d & n \\ \hline 12.0 & 1800 & 6.00 & \end{array} $$

Convert \(25 \pi\) rad (a) to revolutions. (b) to degrees.

Find each missing quantity using \(D \cdot N=d \cdot n\). $$ \begin{array}{cccc} D & N & d & n \\ \hline & 2250 & 9.00 & 1125 \end{array} $$

Convert \(12.0\) revolutions (a) to radians. (b) to degrees.

Find each missing quantity using \(D \cdot N=d \cdot n\). $$ \begin{array}{cccc} D & N & d & n \\ \hline 49.0 & 1860 & & 620 \end{array} $$

A driver pulley of diameter \(6.50\) in. revolves at \(1650 \mathrm{rpm} .\) Find the speed of the driven pulley if its diameter is \(26.0\) in.

Find the angular speed in Problems \(5-10 .\) Number of revolutions \(=7360\) \(t=37.0 \mathrm{~s}\) \(\omega=\) rev/s

A driver pulley of diameter \(25.0 \mathrm{~cm}\) revolves at \(12 \overline{0}\) rpm. At what speed will the driven pulley turn if its diameter is \(48.0 \mathrm{~cm}\) ?

A driver gear has 36 teeth and makes \(85.0 \mathrm{rpm} .\) Find the rpm of the driven gear with 72 teeth.

What horsepower is developed by an engine with torque \(40 \overline{0} \mathrm{lb} \mathrm{ft}\) at \(45 \overline{0} 0 \mathrm{rpm}\) ?

Find the angular speed in Problems \(5-10 .\) Number of revolutions \(=4.00\) \(t=3.00 \mathrm{~s}\) \(\omega=\quad \mathrm{rad} / \mathrm{s}\)

One pulley of diameter \(36.0 \mathrm{~cm}\) revolves at \(60 \overline{0} \mathrm{rpm}\). Find the diameter of the second pulley if it rotates at \(36 \overline{0}\) rpm.

A motor turning at \(1250 \mathrm{rpm}\) is fitted with a gear having 54 teeth. Find the speed of the driven gear if it has 45 teeth.

What torque must be applied to develop \(175 \mathrm{ft} \mathrm{lb} / \mathrm{s}\) of power in a motor if \(\omega=394 \mathrm{rpm} ?\)

Find the angular speed in Problems \(5-10 .\) Number of revolutions \(=325\) \(t=5.00 \mathrm{~min}\) \(\omega=\mathrm{rpm}\)

One pulley rotates at \(45 \overline{0} \mathrm{rpm}\). The diameter of the second pulley is \(15.0 \mathrm{in}\). and rotates at \(675 \mathrm{rpm} .\) Find the diameter of the first pulley.

A gear running at \(25 \overline{0}\) rpm meshes with another revolving at 100 rpm. If the smaller gear has 30 teeth, how many teeth does the larger gear have?

Find the angular velocity of a motor developing \(649 \mathrm{~W}\) of power with torque \(131 \mathrm{~N} \mathrm{~m}\)

An automobile of mass 117 slugs follows a curve of radius \(79.0 \mathrm{ft}\) with a speed of \(49.3 \mathrm{ft} / \mathrm{s}\). What centripetal force is exerted on the automobile while it is rounding the curve?

Find the angular speed in Problems \(5-10 .\) Number of revolutions \(=6370\) \(t=18.0 \mathrm{~s}\) \(\omega=\) rev/s

A pulley with a radius of \(10.0 \mathrm{~cm}\) rotates at \(12 \overline{0}\) rpm. The radius of the second pulley is \(15.0 \mathrm{~cm} ;\) find its rpm.

A high-speed industrial drill develops \(0.500 \mathrm{hp}\) at \(16 \overline{0} 0 \mathrm{rpm} .\) What torque is applied to the drill bit?

Find the centripetal force exerted on a \(7.12-\mathrm{kg}\) mass moving at a speed of \(2.98 \mathrm{~m} / \mathrm{s}\) in a circle of radius \(2.72 \mathrm{~m}\).

Find the angular speed in Problems \(5-10 .\) Number of revolutions \(=6.25\) \(t=5.05 \mathrm{~s}\) \(\omega=\) \(\mathrm{rad} / \mathrm{s} \mathrm{s}\)

Two gears have a speed ratio of \(4.2\) to \(1 .\) If the smaller gear has 15 teeth, how many teeth does the larger gear have?

An engine has torque of \(550 \mathrm{~N} \mathrm{~m}\) at \(8.3 \mathrm{rad} / \mathrm{s}\). What power in watts does it develop?

The centripetal force on a car of mass \(80 \overline{0} \mathrm{~kg}\) rounding a curve is \(6250 \mathrm{~N}\). If its speed is \(15.0 \mathrm{~m} / \mathrm{s}\), what is the radius of the curve?

Convert \(675 \mathrm{rad} / \mathrm{s}\) to rpm.

What size gear should be meshed with a 15 -tooth pinion to achieve a speed reduction of 10 to 3 ?

The centripetal force on a runner is \(17.0 \mathrm{lb}\). If the runner weighs \(175 \mathrm{lb}\) and his speed is \(14.0 \mathrm{mi} / \mathrm{h}\), find the radius of the curve.

Convert 285 rpm to \(\mathrm{rad} / \mathrm{s}\).

A driver gear has 72 teeth and makes \(162 \mathrm{rpm}\). Find the rpm of the driven gear with 81 teeth.

What power (in hp) is developed by an engine with torque 524 lb ft (a) at \(30 \overline{0} 0 \mathrm{rpm} ?\) (b) at 6000 rpm?

An automobile with mass \(1650 \mathrm{~kg}\) is driven around a circular curve of radius \(15 \overline{0} \mathrm{~m}\) at \(80.0 \mathrm{~km} / \mathrm{h}\). Find the centripetal force of the road on the automobile.

Convert \(136 \mathrm{rpm}\) to \(\mathrm{rad} / \mathrm{s}\).

A driver gear with 60 teeth makes \(1600 \mathrm{rpm}\). How many teeth must the driven gear have if it makes 480 rpm?

Find the angular velocity of a motor developing \(650 \mathrm{~W}\) of power with a torque of \(130 \mathrm{~N} \mathrm{~m}\).

A cycle of mass \(510 \mathrm{~kg}\) rounds a curve of radius \(4 \overline{0} \mathrm{~m}\) at \(95 \mathrm{~km} / \mathrm{h}\). What is the centripetal force on the cycle?

Convert \(88.4 \mathrm{rad} / \mathrm{s}\) to rpm.

What size gear should be meshed with a 20 -tooth pinion to achieve a speed reduction of 3 to 1 ?

A drill develops \(0.500 \mathrm{~kW}\) of power at \(18 \overline{0} 0 \mathrm{rpm} .\) What torque is applied to the drill bit?

What is the centripetal force exerted on a rock with mass \(3.2 \mathrm{~kg}\) moving at \(3.5 \mathrm{~m} / \mathrm{s}\) in a circle of radius \(2.1 \mathrm{~m} ?\)

A motor turns at a rate of \(11.0\) rev/s. Find its angular speed in rpm.

What size pulley should be placed on a countershaft turning \(15 \overline{0}\) rpm to drive a grinder with a \(12.0-\mathrm{cm}\) pulley that is to turn at \(120 \overline{0}\) rpm?

A motor turning at \(15 \overline{0} 0\) rpm is fitted with a gear having 60 teeth. Find the speed of the driven gear if it has 40 teeth.

What power is developed by an engine with torque \(75 \overline{0} \mathrm{~N} \mathrm{~m}\) applied at \(45 \overline{0} 0 \mathrm{rpm} ?\)