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physics
mechanics

Questions and Answers of Mechanics

An airplane propeller is rotating at 1900 IpI11 (rev/min). (a) Compute the propeller's angular velocity in rad/s. (b) How many seconds does it take for the propeller to turn through 35°?
The angular velocity of a flywheel obeys the equation wc(t) = A + Bt2 , where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (a) What are the units
A fan blade rotates with angular velocity given by wu (t) =Y - Bt2, where Y = 5.00 rad/s and p = 0.800 rad/s3. (a) Calculate the angular acceleration as a function of time. (b) Calculate the
A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to Ii(t) = Yt + pt, where 'Y = 0.400rad/s and p = 0.0l20rad/s3. (a) Calculate
At t = 0 the current to a de electric motor is reversed, resulting in an angular displacement of the motor shaft given by Ii(t) = (250rad/s)t - (20.0rad/s2)t2 - (1.50rad/s)t. (a) At what time is
The angle 6 through which a disk drive turns is given by 6(t) = a + ht - ct3, where a, h, and c are constants, t is in seconds, and6isinradians. When t = 0,6 = ."./4 rad and the angular velocity is
A wheel is rotating about an axis that is in the z-direction. The angular velocity wt is -6.00 rad/s at f = 0, increases linearly with lime, and is +8.00 m/s at f = 7.00 s. We have taken
A bicycle wheel has an initial angular velocity of 1.50 rad/ s. (a) If its angular accelera1ion is constant and equal to 0.300 rad/s3, what is its angular velocity at t = 2.50 s? (b) Through what
An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s. (a) Find the angular accelera1ion in rev/s' and the number of revolutions made
The rotating blade of a blender turns with constant angular acceleration 1.50 rad/s. (a) How much time does it take to reach an angular velocity of 36.0 rad/s, starting from rest? (b) Through how
(a) Derive Eq. (9.12) by combining Eqs. (9.7) and (9.11) to eliminate f (b) The angular velocity of an airplane propeller increases from 12.0 rad/s to 16.0 rad/s while turning through 7.00 rad. What
A turntable rotates with a constant 2.25 rad/s3 angular acceleration. After 4.00 s it has rotated through an angle of 60.0 rad. What was the angular velocity of the wheel at the beginning of the
A circular saw blade 0.200 m in diameter starts from rest. In 6.00 s it accelerates with constant angular acceleration to an angular velocity of 140 rad/s. Find the angular acceleration and the angle
A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the
A computer disk drive is turned on starting from rest and has constant angular acceleration. If it took 0.750 s for the drive to make its second complete revolution, (a) How long did it take to
A safety device brings the blade of a power mower from an initial angular speed of wt to rest in 1.00 revolution. At the same constant accelera1ion, how many revolutions would it take the blade to
A straight piece of reflecting tape extends from the center of a wheel to its rim. You darken the room and use a camera and strobe unit that flash once every 0.050 s to take pictures of the wheel as
At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It has a constant angular acceleration of 30.0 rad/s3 until a circuit breaker trips at t = 2.00 s. From then on, it turns through 432
In a charming 19th century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 2.50 m in diameter (Fig. 9.28). The elevator is raised and lowered
Using astronomical data from Appendix F, along with the fact that the earth spins on its axis once per day, calculate (a) The earth's orbital angular speed (in rad/s) due to its motion around the
Compact Disc 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
A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s2. At the instant the wheel has computed its second revolution compute the radial
Ultra centrifuge find the required angular speed (in rev/min) of an ultracentrifuge for the radial acceleration of a point 2.50 cm from the axis to equal 400,000g (that is, 400,000 limes the
A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2, compute the magnitude of the tangential acceleration, the radial
An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2, (a) Compute the angular
Centrifuge an advertisement claims that a centrifuge takes up only 0.127 m of bench space but can produce a radial acceleration of 3000g at 5000 rev/min. Calculate the required radius of the
(a) Derive an equation for the radial acceleration that includes v and Cd, but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of 0.500 m/s2
Electric Drill according to the shop manual, when drilling a 12.7-mm-diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1250 rev/min. For a 12.7-mm-diameter drill bit turning
At t = 3.00 s a point on the rim of a 0.200-m-radius wheel has a tangential speed of 50.0 m/s as the wheel slows down with a tangential acceleration of constant magnitude 10.0 m/s2. (a) Calculate
The spin cycles of a washing machine have two angular speeds, 423 rev/min and 640 rev /min. The internal diameter of the drum is 0.470 m. (a) What is the ratio of the maximum radial force on the
You are to design a rotating cylindrical axle to lift 800-N buckets of cement from the ground to a rooftop 7S.0 m above the ground. The buckets will be attached to a hook on the free end of a cable
While riding a multi speed bicycle, the rider can select the radius of the rear sprocket that is fixed to the rear axle. The front sprocket of a bicycle has radius 12.0 cm. If the angular speed of
Four small spheres each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by extremely light rods (Fig. 9.29). Find the moment of 0 inertia
Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular
Small blocks, each with mass m, are clamped at the ends and at the center of a rod of length L and negligible mass. Compute the moment of inertia of the system about an axis perpendicular to the rod
A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.500 kg and can be treated as point masses. Find the moment of
A twirler's baton is made of a slender metal cylinder of mass M and length L. Each end has a rubber cap of mass m, and you can accurately treat each cap as a particle in this problem. Find the total
A wagon wheel is constructed as shown in Fig. 9.30. The radius of the wheel is 0.300 m, and the rim has mass 1.40 kg. Each of the eight spokes that lie along a diameter and are 0.300 m long has mass
A uniform disk of radius R is cut in half so that the remaining half bas mass M (Fig. 931a). (a) What is the moment of inertia of this half about an axis perpendicular to its plane through point A?
A compound disk of outside diameter 140.0 cm is made up of a uniform solid disk of radius 50.0 cm and area density 3.00 g/cm2 surrounded by a concentric ring of inner radius 50.0 cm, outer radius
An airplane propeller is 2.08 m in length (from tip to tip) with mass 117 kg and is rotating at 2400 rpm {rev/min} about an axis through its center you can model the propeller as a slender rod. (a)
Energy from the Moon Suppose that some time in the furor we decide to tap the moon's rotational energy for use on earth, in additional to the astronomical data in Appendix F, you may need to know
You need to design an industrial turntable that is 60.0 cm in diameter and bas a kinetic energy of 0.250 J when turning at 45.0 rpm {rev/min}. (a) What must be the moment of inertia of the
The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?
A light, flexible rope is wrapped several times around a hollow cylinder, with a weight of 40.0 N and a radius of 0.25 m that rotates without friction about a fixed horizontal axis. The cylinder is
Energy is to be stored in a 70.G-kg flywheel in the shape of a uniform solid disk with radius R = 1.20 m. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a
Suppose the solid cylinder in the apparatus descended in Example 9.9 (Section 9.4) is replaced by a thin-walled, hollow cylinder with the same mass M and radius R. The cylinder is attached to the
A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A l.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Fig.
A bucket of mass m is tied to a mass less cable that is wrapped around the outer rim of a frictionless uniform pulley of radius R, similar to the system shown in Fig. 9.32. In terms of the stated
How I Scales if we multiply all the design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f3. (a) By what factor will its moment of inertia be multiplied?
A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0• with the floor. Worker posses the ladder up against the wall until it is vertical. How much
A uniform 3.00-kg rope 24.0 m long lies on the ground at the top of a vertical cliff. A mountain climber at the top lets down half of it to help his partier climb up the cliff. What was the change in
Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass M and radius R about an axis perpendicular to the hoop's plane at an edge.
About what axis will a uniform, balsa-wood sphere have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius, with the axis along a diameter
Use the parallel-axis theorem to show that the moments of inertia given in parts (a) and (b) of Table 9.2 are consistent.
A thin, rectangu1ar sheet of metal has mass M and sides of length a and b. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane
(a) For the thin rectangular plate shown in part (d) of Table 9.2, find the moment of inertia about an axis that lies in the plane of the plate, passes through the center of the plate, and is
A thin uniform rod of mass M and length L is bent at its center so that the two segments are now perpendicular to each other Find its moment of inertia about an axis perpendicular to its plane and
Using the information in Table 9.2 and the parallel-axis theorem, find the moment of inertia of the slender rod with mass M and length L shown in Fig. 9.23 about an axis through 0, at an arbitrary
Use Eq. (9.20) to calculate the moment of inertia of a uniform, solid disk with mass M and radius R for an axis perpendicular to the plane of the disk and passing through its center.
Use Eq. (9.20) to calculate the moment of inertia of a slender, uniform rod with mass M and length L about an axis at one end, perpendicular to the rod.
A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = 'YX, where 'Y has units of kg/m2. (a) Calculate the total mass
Sketch a wheel lying in the plane of your paper and rotating counter clock wise. Choose a point on the rim and draw a vector 1 from the center of the wheel to that point. (a) What is the direction
Trip to Mars you are wailing on a project with NASA to launch a rocket to Mars, with the rocket blasting off from earth when earth and Mars are aligned along a straight line from the sun. If Mars is
A roller in a printing press turns through an angle θ(t} given by θ(t} = Yt2 - Bt, where Y = 3.20rad/s2 and p = 0.500 rad/s. (a) Calculate the angular velocity of the roller as a function
A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center it has very thin but strong string wrapped around its rim, and the string is attached to a ball that is
When a toy car is rapidly scooted across the floor, it stores energy in a flywheel. The car has mass 0.180 kg, and its flywheel has moment of inertia 4.00 X 10-5 kg . m2• The car is 15.0 cm long.
A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 3.00 m/s2 on a circular test track of radius 60.0 m. treat the car as a
Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (Fig.
A vacuum cleaner belt is looped over a shaft of radius 0.45 cm and a wheel of radius 2.00 cm. The arrangement of the belt, shaft, and wheel is similar to that of the chain and sprockets in Fig. 9.14.
The motor of a table saw is rotating at 3450 rev/min. A pulley attached to the motor shaft drives a second pulley of half the diameter by means of a V-belt. A circular saw blade of diameter 0.208 m
A wheel changes its angular velocity with a constant angular acceleration while rotating about a fixed axis through its center (a) Show that the change in the magnitude of the radial acceleration
A sphere consists of a solid wooden ball of uniform density 800 kg/m' and radius 0.20 m and is covered with a thin coating of lead foil with area density 20 kg/m2. Calculate the moment of inertia of
Estimate your own moment of inertia about a vertical axis through the center of the top of your head when you are standing up straight with your arms outstretched. Make reasonable approximations and
A thin uniform rod 50.0 cm long with mass 0.320 kg is bent at its center into a V shape, with a 70.00 angle at its vertex. Find the moment of inertia of this V-shaped object about an axis
It has been argued that power plants should make use of off peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle
While redesigning a rocket engine, you want to reduce its weight by replacing a solid spherical part with a hollow spherical shell of the same size. The parts rotate about an axis through their
The earth, which is not a uniform sphere, has a moment of inertia of 0.3308MR2 about an axis through its north and south poles. It takes the earth 86,164 s to spin once about this axis. Use Appendix
A uniform, solid disk with mass m and radius R is pivoted about a horizontal axis through its center. A small object of the same mass m is glued to the rim of the disk. If the disk is released from
A metal sign for a car dealership is a thin, uniform right triangle with base length b and height h. The sign has mass M. (a) What is the moment of inertia of the sign for rotation about the side
Measuring 1 as an intern with an engineering firm, you are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you were a good physics
A meter stick with a mass of 0.160 kg is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released As it swings
Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R. The cylinder rotates without friction about a horizontal axle along the cylinder axis.
The pulley in Fig. 9.35 has radius R and a moment of inertia l. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block
The pulley in Fig. 936 has radius 0.160 m and moment of inertia 0.480 kg m2. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it
You hang a thin hoop with radius R over a nail at the rim of the hoop. You displace it to the side (within the plane of the hoop) through an angle fJ from its equilibrium position and let it go. What
A passenger bus in Zurich, Switzerland, derived its motive power from the energy stored in a large flywheel. The wheel was brought up to speed periodically, when the bus stopped at a station, by an
Two metal disks, one with radius R, = 2.50 cm and mass M, = 0.80 kg and the other with radius R2 = 5.00 cm and mass M, = 1.60 kg, are welded together and mounted on a frictionless axis through their
In the cylinder and mass combination described in Example 9.9 (Section 9.4), suppose the fa1ling mass m is made of ideal rubber, so that no mechanical energy is lost when the mass hits the ground.
In the system shown in Fig. 9.18, a 12.O-kg mass is released from rest and falls, causing the uniform 1O.0-kg cylinder of diameter 30.0 cm to turn about a frictionless axle through its center. How
In Fig. 9.38, the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder. passes over the pulley, and
A thin, flat, uniform disk has mass M and radius R_ A circular hole of radius R/4, centered at a point R/2 from the disk's center, is then punched in the disk. (a) Find the moment of inertia of the
A pendulum is made of a uniform solid sphere with mass M and radius R suspended from the end of a light rod. The distance from the pivot at the upper end of the rod to the center of the sphere is L.
Perpendicular-Axis Theorem Consider a rigid body that is a thin, plane sheet of arbitrary shape. Take the body to lie in the xy-plane and let the origin 0 of coordinates be located at any point
A thin, uniform rod is bent into a square of side length a. If the total mass is M, find the moment of inertia about an axis through the center and perpendicular to the plane of the square. (Hint:
A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, p = ar, where a is a positive constant (a) Calculate the moment of inertia of the
Neutron Stars and Super nova Remnants the Crab Nebula is a cloud of glowing gas about 10 light-years across, located about 6500 light years from the earth (Fig. 9.39). It is the remnant of a star
The moment of inertia of a sphere with uniform density about an axis through its center is 2/5 MR = 0.400MR'. Satellite observations show that the earth's moment of inertia is 0.330SMR, Geophysical
Calculate the moment of inertia of a uniform solid cone about an axis through its center (Fig. 9.40). The cone has mass M and altitude h. The radius of its circular base is R.
On a compact disc (CD), music is coded in a pattern of tiny pits arranged in a track that spirals outward toward the rim of the disc. As the disc spins inside a CD player, the track is scanned at a

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