Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 13, Problem 74PQ
When a person jumps off a diving platform, she imparts some amount of
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Divers change their body position in midair while rotating about their center of mass. In one dive, the diver leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of inertia of the diver in a straight position is 14 kg m2 and in a tucked position is 4.0 kg m2, by what factor is her angular velocity when tucked greater than when straight?
A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does:
O both go around with equal angular velocities but in opposite directions.
O the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground.
O the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground.
O the platform doesn't rotate.
Consider a wooden rectangular slab of mass M, length L, and width W nailed vertically to a wall. The nail is located approximately at the middle of the top edge (see Figure 1). You use a hammer to hit the bottom right corner with an average force F, and the hammer is contact with the slab for a small time Δt. The moment of inertia for the axis passing through the center of the slab, pointing away from the wall, is I=(1/12)M(L^2+W^2).
a) What is the angular speed of the slab about the nail just after you have hit the slab? Explain every part of your working carefully; in particular, state any assumptions you make. Hint: consider ττ=dL/dt. Use the torque due to the force exerted by the hammer.
Chapter 13 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 13.1 - CASE STUDY When Is Energy Conserved? Under what...Ch. 13.6 - Figure 13.24 shows a particle with momentum p....Ch. 13.7 - Prob. 13.3CECh. 13.7 - Prob. 13.4CECh. 13.7 - Prob. 13.5CECh. 13 - Prob. 1PQCh. 13 - Prob. 2PQCh. 13 - A Frisbee flies across a field. Determine if the...Ch. 13 - Prob. 4PQCh. 13 - Prob. 5PQ
Ch. 13 - Rotational Inertia Problems 5 and 6 are paired. 5....Ch. 13 - A 12.0-kg solid sphere of radius 1.50 m is being...Ch. 13 - A figure skater clasps her hands above her head as...Ch. 13 - A solid sphere of mass M and radius Ris rotating...Ch. 13 - Suppose a disk having massMtot and radius R is...Ch. 13 - Problems 11 and 12 are paired. A thin disk of...Ch. 13 - Given the disk and density in Problem 11, derive...Ch. 13 - A large stone disk is viewed from above and is...Ch. 13 - Prob. 14PQCh. 13 - A uniform disk of mass M = 3.00 kg and radius r =...Ch. 13 - Prob. 16PQCh. 13 - Prob. 17PQCh. 13 - The system shown in Figure P13.18 consisting of...Ch. 13 - A 10.0-kg disk of radius 2.0 m rotates from rest...Ch. 13 - Prob. 20PQCh. 13 - Prob. 21PQCh. 13 - In Problem 21, what fraction of the kinetic energy...Ch. 13 - Prob. 23PQCh. 13 - Prob. 24PQCh. 13 - Prob. 25PQCh. 13 - A student amuses herself byspinning her pen around...Ch. 13 - The motion of spinning a hula hoop around one's...Ch. 13 - Prob. 28PQCh. 13 - Prob. 29PQCh. 13 - Prob. 30PQCh. 13 - Sophia is playing with a set of wooden toys,...Ch. 13 - Prob. 32PQCh. 13 - A spring with spring constant 25 N/m is compressed...Ch. 13 - Prob. 34PQCh. 13 - Prob. 35PQCh. 13 - Prob. 36PQCh. 13 - Prob. 37PQCh. 13 - Prob. 38PQCh. 13 - A parent exerts a torque on a merry-go-round at a...Ch. 13 - Prob. 40PQCh. 13 - Today, waterwheels are not often used to grind...Ch. 13 - Prob. 42PQCh. 13 - A buzzard (m = 9.29 kg) is flying in circular...Ch. 13 - An object of mass M isthrown with a velocity v0 at...Ch. 13 - A thin rod of length 2.65 m and mass 13.7 kg is...Ch. 13 - A thin rod of length 2.65 m and mass 13.7 kg is...Ch. 13 - Prob. 47PQCh. 13 - Two particles of mass m1 = 2.00 kgand m2 = 5.00 kg...Ch. 13 - A turntable (disk) of radius r = 26.0 cm and...Ch. 13 - CHECK and THINK Our results give us a way to think...Ch. 13 - Prob. 51PQCh. 13 - Prob. 52PQCh. 13 - Two children (m = 30.0 kg each) stand opposite...Ch. 13 - A disk of mass m1 is rotating freely with constant...Ch. 13 - Prob. 55PQCh. 13 - Prob. 56PQCh. 13 - The angular momentum of a sphere is given by...Ch. 13 - Prob. 58PQCh. 13 - Prob. 59PQCh. 13 - Prob. 60PQCh. 13 - Prob. 61PQCh. 13 - Prob. 62PQCh. 13 - A uniform cylinder of radius r = 10.0 cm and mass...Ch. 13 - Prob. 64PQCh. 13 - A thin, spherical shell of mass m and radius R...Ch. 13 - To give a pet hamster exercise, some people put...Ch. 13 - Prob. 67PQCh. 13 - Prob. 68PQCh. 13 - The velocity of a particle of mass m = 2.00 kg is...Ch. 13 - A ball of mass M = 5.00 kg and radius r = 5.00 cm...Ch. 13 - A long, thin rod of mass m = 5.00 kg and length =...Ch. 13 - A solid sphere and a hollow cylinder of the same...Ch. 13 - A uniform disk of mass m = 10.0 kg and radius r =...Ch. 13 - When a person jumps off a diving platform, she...Ch. 13 - One end of a massless rigid rod of length is...Ch. 13 - A uniform solid sphere of mass m and radius r is...Ch. 13 - Prob. 77PQCh. 13 - A cam of mass M is in the shape of a circular disk...Ch. 13 - Prob. 79PQCh. 13 - Consider the downhill race in Example 13.9 (page...Ch. 13 - Prob. 81PQ
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- Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in which you calculate the necessary angular velocity that assures the riders will not slide down the wall. Include a free body diagram of a single rider. Among the variables to consider are the radius of the cylinder and the coefficients of friction between the riders’ clothing and the wall.arrow_forwardA turntable with a mass of 12 kg and a radius of 2 meters spins at a constant angular velocity of 140 rpm. A 500-gram scoop of uniformly-dense ice cream falls onto the turntable, so the scoop's center of mass is one meter away from the turntable's center. The scoop forms a hemisphere and has a radius of 4 cm. If there's no friction between the brick and ice cream scoop and they spin at the same angular speed, what is their final angular speed, in rev/min or in rad/s? Justify your answer with your rationale and equations used. Moments of Inertia: Idisk =MR for rotation about its center of mass parallel to the z-axis. %3D Ihemisphere = MR for rotation about its center of mass parallel to the z-axis. Edit View Ansert Format Tools Table COREIarrow_forwardLily is a 50 kg diver. At the instant of takeoff, her angular momentum about her longitudinal axis is 20 kgm2/s. Her radius of gyration about the longitudinal axis is 0.4 m at this instant. During the dive, Lily tucks and reduces her radius of gyration about the longitudinal axis to 0.2 m. At takeoff, what is Lily’s moment of inertia about her longitudinal axis? At takeoff, what is Lily’s angular velocity about her longitudinal axis? After Lily tucks, what is her moment of inertia about her longitudinal axis? After Lily tucks, what is her angular velocity about her longitudinal axis?arrow_forward
- Now let's apply our definition of angular momentum to a specific object. A mobile sculpture is suspended from the ceiling of an airport terminal building. It consists of two metal spheres, each with mass 2.0 kgkg, connected by a uniform metal rod with mass 3.0 kgkg and length s=4.0ms=4.0m. The assembly is suspended at its midpoint by a wire and rotates in a horizontal plane, making 3.0 revolutions per minute. Find the angular momentum and kinetic energy of the assembly. Part A - What would the kinetic energy of the sculpture be if the rod was twice as long but it still had the same angular momentum as in the example? Express your answer in joules to two significant figures.arrow_forwardConsider the system shown in (Figure 1). Figure 6 m B 4 m F C 4 m 6 m 1 of 1 > Determine the x, y, and components of the moment of the force of F = 700 N about point A Enter the components of the moment separated by commas. Express your answers newton-meters to three significant figures. Mz, My, M₂ = Submit Provide Feedback VAΣo↓ vec Request Answer ? N.marrow_forwardConsider the system shown below where four point masses are connected to each other by massless rods. Two of the masses are m = 3 kg and the other two have the masses of M = 2 kg. If a = 1.4 m, b = 1.3 m and the system rotates about x-axis, determine the moment of inertia of the system. Express your answer in units of kg. m² using one decimal place. Answer: M a m m b b a M-xarrow_forward
- - A subway train consisting of 3 cars moves on a straight track with a velocity of 1.1 meters per second. The mass of each car 3,119 kilograms. What is the total linear momentum of the train? Use kg m/s as unit. - A wind turbine has a moment of inertia of 1,265 kg m2. What is the angular momentum L of the turbine if its period of rotation is 3.16 seconds? Note, use "kg m2/s" (without the quotes) for the unit of the rotational momentum in your answer. - A 0.14 kg solid billiard ball with a radius of 0.1 m is rolling on a pool table with a speed of 1.12 m/s without slipping. Find the angular momentum of the ball. (unit in kg m2/s)arrow_forwardA ring (mass 4 M, radius 2 R) rotates in a CCw direction with an initial angular speed 2 w. A disk (mass 4 M, radius 2 R) rotates in a CW direction with initial angular speed 2 w. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCw direction. What is the initial angular momentum Lj of the ring+disk system? Write your answer in terms of MR2W. MR2W Submit Answer Tries 0/3 What is the final angular velocity wf of the ring+disk system? Write your answer in terms of w. Submit Answer Tries 0/3arrow_forwardConsider this: Both scenario has same length of surface of 60 meters. A. A 50-kg object is located exactly 30 meters from both side of the surface. B A 75-kg object is located 20 meters from the left edge of the surface. Compute the torque, draw a free body diagram and write a short description about it.arrow_forward
- Three identical particles of mass m are making a common uniform circular motion with the period T inside a torus of Y10Q3 central radius R. We neglect the size of the balls. The three balls always form three vertices of a equlateral triangle. RO Determine the following quantities for this three-body system. Orbital angular momentum about the origin O. B Net force C Net torque D Kinetic energyarrow_forwardNow let's apply our definition of angular momentum to a specific object. A mobile sculpture is suspended from the ceiling of an airport terminal building. It consists of two metal spheres, each with mass 2.0 kg, connected by a uniform metal rod with mass 3.0 kg and length s=4.0ms=4.0m. The assembly is suspended at its midpoint by a wire and rotates in a horizontal plane, making 3.0 revolutions per minute. Find the angular momentum and kinetic energy of the assembly. solution: k= 0.96J a) What would the kinetic energy of the sculpture be if the rod was three times as long but it still had the same angular momentum as in the example?arrow_forwardA horizontal circular platform rotates counterclockwise about its axis at the rate of 0.897 rad/s. You, with a mass of 74.1 kg. walk clockwise around the platform along its edge at the speed of 1.15 m/s with respect to the platform. Your 20.3 kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 17.3 kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 92.7 kg and radius 1.99 m. Calculate the total angular momentum Lot of the system. Lot 2 kg-m²/sarrow_forward
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