A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with a frictionless pivot and a string as shown in the diagram above. The initial angle of the rod with respect to the wall, is = 39º. The string is then cut. The moment of inertia of a rod about an axis through one end is 1/3ML². What is the angular acceleration of the rod, a, immediately after the string is cut? A: a = 6.17 rad/s² What is the angular velocity w of the rod when it is horizontal (0 = 90°)? A: w 3.9 rad/sec 0 ΔΕ(m) = 0 T net, P = la 2 2 Iw₁² + MgYcm1 = Iw² + MgYcm0
Q: The uniform thin rod in the figure below has mass M = 5.00 kg and length L = 3.45 m and is free to…
A:
Q: A spinning figure skater who brings their arms close in to their body will then spin faster. The…
A:
Q: A spinning figure skater who brings their arms close in to their body will then spin faster. The…
A: Given Mass of the skater is M=50 kg Length of the arm is Ri=0.8 Ω Initial angular speed is ωi=2…
Q: Four particles, each of mass 0.13 kg, are placed at the vertices of a square with sides of length…
A: m=0.13 Kg a=0.58 m
Q: As the figure shows, a homogeneous rod of mass 1kg and length L = 2 m is nailed to the wall at its…
A: We will first write an expression for torque and use it to find the net torque due to three given…
Q: The figure shows three 0.0105 kg particles that have been glued to a rod of length L=6.50 cm and…
A:
Q: Four particles, each of mass 0.14 kg, are placed at the vertices of a square with sides of length…
A:
Q: A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the…
A: Given that: Radius of the circle, r=2.3 cmLength of the string, L=74 cmAngular acceleration, α=+13…
Q: A typical propeller of a turbine used to generate electricity from the wind consists of three blades…
A: Given: Length of blade L=30 m Mass of blade m=400 Kg Angular speed w= 28 rev/min To find: a) Angular…
Q: A yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller…
A:
Q: The figure shows three 0.0133 kg particles that have been glued to a rod of length L-5.84 cm and…
A:
Q: The uniform thin rod in the figure below has mass M- 2.50 kg and length L 2.29 m and is free to…
A:
Q: In the figure here, three particles of mass m = 0.017 kg are fastened to three rods of length d=…
A:
Q: A motorcyclist is traveling along a road and accelerates for 4.11 s to pass another cyclist. The…
A:
Q: A rigid body is made of three identical thin rods, each with length L = 0.320 m, fastened together…
A: The information given about the system includes, 1. Three rods each of length L=0.320 m, arranged in…
Q: The figure shows three 0.0113 kg particles that have been glued to a rod of length L=6.07 cm and…
A: The mass of each of the particle is m=0.0113 kg The length of the rod is L=6.07 cm
Q: The figure shows three 0.0121 kg particles that have been glued to a rod of length L=6.41 cm and…
A:
Q: Consider the diagram below. The axle radius is 1 m and the wheel radius is 4 m. A 1600-N load is…
A: Given The axle radius = 1 m the wheel radius = 4 m. load = 1600-N The moment of inertia of the…
Q: In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a…
A:
Q: In the figure here, three particles of mass m = 0.022 kg are fastened to three rods of length d =…
A: Given data:mass of each particle (m) = 0.017 Kglength of each rod (d) = 0.13 mAngular speed ω= 0.950…
Q: The figure shows three 0.0138 kg particles that have been glued to a rod of length L=5.71 cm and…
A:
Q: A uniform spherical shell of mass M = 20.0 kg and radius R=0.360 m can rotate about a vertical axis…
A:
Q: A hollow, spherical shell with mass 2 kg rolls without slipping down a 37 slope. The acceleration…
A: The acceleration for the hollow sphere is given as a=35gsinθ
Q: In the figure, two particles, each with mass m = 0.90 kg, are fastened to each other, and to a…
A: Given Data: Mass of the particle (m) = 0.90 kg.Length (d) = 5.6 cm = 0.056 m.Mass of the rods (M) =…
Q: In the figure. two particles. each with mass m 0.95 kg. are fastened to each other, and to a…
A: Given,mass of the each particle, m = 0.95 kglength of the rod, d = 5.8 cmmass of the rod, M = 1.0…
Q: A flywheel with a radius of 0.240 mm starts from rest and accelerates with a constant angular…
A: Radius is r=0.240 mm Angular acceleration is α=0.780 rad/s2 Initially object is at rest so its…
Q: A uniform spherical shell of mass M = 3.8 kg and radius R = 7.6 cm can rotate about a vertical axis…
A:
Q: The figure shows three 0.0120 kg particles that have been glued to a rod of length L=6.36 cm and…
A:
Q: The figure shows three 0.0132 kg particles that have been glued to a rod of length L=6.18 cm and…
A: a)The total moment of inertia of the system is,
Q: A rigid body is made of three identical rods, each with length L = 0.775 m, fastened together in the…
A:
Q: A uniform rod of mass M=6 kg and length L=3 m with a particle of mass m=2 kg attached to its one end…
A: Mass of the rod M=6kgLength of the rod, L=3mMass of the particle, m=2kgAngle made by the rod with…
Q: The figure shows three 0.0133 kg particles that have been glued to a rod of length L=6.23 cm and…
A:
Q: Two wheels A and B in the figure are connected by a belt that does not slip. The radius of B is 6.03…
A:
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
- A 50.0 kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 2.80 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.250 rad/s relative to the earth. The radius of the turntable is Part A 3.50 m, and its moment of inertia about the axis of rotation is Find the magnitude of the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can model the runner as a particle.) 80.0 kg m2 Express your answer in radians per second. ■ AX中 rad/sThe wheel of radius R shown below consists of a hoop of massm and two thin rods, each of mass M. Calculate the moment of inertia of the wheel about an axis going through its center, perpendicular to the plane of the hoop, for the values listed below. Express your answer in kg m2 to three significant figures. R= 2.28 m m = 0.372 kg M= 0.288 kgThe left-hand end of a uniform rod of length L and mass m is attached to a vertical wall by a frictionless hinge. The rod is held at an angle θ above the horizontal by a horizontal wire that runs between the wall and the right-hand end of the rod. The wire breaks and the rod rotates about the hinge. What is the angular speed of the rod as the rod passes through a horizontal position? (Express your answer in terms of some or all of the variables m, g, L, θ.)
- a top with radius 10cm, mass 2 kg has a string around the edge and is initially at rest. assume the top can be reasonably approximated as a solid cylinder. the top is held in place as the string is pulled. the string applies a force of 10N tangential to the edge for 2s. what is the angular velocity (in radians per second) of the top after 3 seconds? what is the angular momentum of the top after the string is pulled? after the string is pulled, the top is released. it travels away from its initial position at a linear velocity of 10m/s. what is the rotational velocity (in radians per s) at this top? assume no frictionA yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle. Part (a) Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius. Part (b) Find the linear speed V of the yo-yo, after it has descended a distance H. Part (c) Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.39 mFour particles, each of mass 0.39 kg, are placed at the vertices of a square with sides of length 0.57 m. The particles are connected by rods of negligible mass. This rigid body can rotate in a vertical plane about a horizontal axis A that passes through one of the particles. The body is released from rest with rod AB horizontal, as shown in the figure. (a) What is the rotational inertia of the body about axis A? (b) What is the angular speed of the body about axis A at the instant rod AB swings through the vertical position? Rotation аxis A B (a) Number i Units (b) Number i Units
- A spool consists of a cylinder with two circular disks glued on either end. It has mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R. String is wrapped tightly around the cylinder. The spool is placed on its side and the string is pulled with force T from an angle 0 above the horizontal. The spool rolls without slipping. (a) Compute the angular acceleration about the center of mass at the instant the force is first applied. (b) Which way does the spool roll, right or left? Does this depend on the properties of the spool and/or the angle 0? If so, find a formula. Note: if you did not succeed in part 1, you can still get partial credit here for a correct qualitative discussion.A uniform thin rod of mass ?=3.47 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass ?=0.277 kg, are attached to the ends of the rod. What must the length ? of the rod be so that the moment of inertia of the three-body system with respect to the described axis is ?=0.987 kg·m2 ?Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rb=2R are connected by a thin, uniform rod of length L=2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form.
- The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.156 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks = 0.0525 m thick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same ta %3D moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? = PA rdModern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared. b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.The uniform thin rod in the figure below has mass M = 2.50 kg and length L = 2.87 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end. HINT L/2 × CG M O (a) the rod's angular acceleration (in rad/s²) rad/s² (b) the tangential acceleration of the rod's center of mass (in m/s²) (c) m/s² the tangential acceleration of the rod's free end (in m/s²) m/s²