Concept explainers
Write down Newton’s second law for each spool. Express your answer in terms of the mas of each spool (m), the acceleration of the center of mass of each spool
Write down the rotational analogue to Newton’s second law for each spool. Express your answer in terms of the relevant rotational quantities, that is, in terms of the
Learn your wayIncludes step-by-step video
Chapter 4 Solutions
Tutorials in Introductory Physics
Additional Science Textbook Solutions
University Physics Volume 1
Life in the Universe (4th Edition)
College Physics: A Strategic Approach (3rd Edition)
Essential University Physics (3rd Edition)
Physics for Scientists and Engineers with Modern Physics
Conceptual Integrated Science
- State the relation between torque and angular momentum in rotational motion. A 1.8-kg particle moves in a circle of radius 3.4 m. As you look down on the plane of its orbit, it is initially moving clockwise. If we call the clockwise direction positive, its angular momentum relative to the center of the circle varies with time according to L(t) = 3 – 4t. Find the magnitude and direction of the torque acting on the particle.arrow_forwardA solid, uniform disk of mass M and radius a may be rotated about any axis parallel to the disk axis, at variable distances from the center of the disk. ( Figure 1) Figure a ‒‒‒‒‒‒ 1 of 1 Part A What is Icm, the moment of inertia of the disk around its center of mass? You should know this formula well. Express your answer in terms of given variables. V— ΑΣΦ Icm = Submit Part B T (d) = If you use this disk as a pendulum bob, what is T (d), the period of the pendulum, if the axis is a distance d from the center of mass of the disk? Express the period of the pendulum in terms of given variables. ► View Available Hint(s) Submit Part C Request Answer maximum minimum Submit The period of the pendulum has an extremum (a local maximum or a local minimum) for some value of d between zero and infinity. Is it a local maximum or a local minimum? ► View Available Hint(s) ΑΣΦ Provide Feedback wwwww.. ? Part D Complete previous part(s) ? Nextarrow_forwardPart C In which case is less force required? case A O case Barrow_forward
- Figure X y₁arrow_forwardThe system is made up of the 1-m, 7.1-kg uniform rod AB and the two uniform disks (each of 0.17 m radius and 1.9 kg mass). If the system is released from rest when = 63°, determine the total external work done to this system when rod AB has just become horizontal. Assume the disks roll without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s². B m Ө Your Answer: Answer units Barrow_forwardA cord is wrapped around the rim of a solid uniform wheel 0.200 m in radius and of mass 7.20 kg. A steady horizontal pull of 30.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. Part A Compute the angular acceleration of the wheel. Express your answer in radians per second squared. la| = 17.14 rad/s? Part B Compute the acceleration of the part of the cord that has already been pulled off the wheel. Express your answer in radians per second squared. Eνα ΑΣφ ? la| = m/s? + Part C Find the magnitude of the force that the axle exerts on the wheel, Express your answer in newtons. ανα ΑΣφ F = Narrow_forward
- Time left 0:56:53 1. For the typical Oar (shown in the figure below) used in rowing boats, select an engineering material that would be lightweight and stiff. It must be strong enough to carry the bending moment exerted by the rower without breaking and it must have the right stiffness. The function is identified to be a beam, loaded in bending. The length L and stiffness S are fixed by the design, leaving the radius R as the only dimensional variable. The mass m of the oar is minimized by choosing materials with large values of the material index. E1/2 %3Darrow_forwardA uniform disk of mass 19 kg and radius 0.6 m is free to rotated about an axis perpendicular to its center. A constant force of size 165 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 181 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forward1. a) Define a holonomic constraint and explain the impact of such constraints on the number of degrees of freedom of a system. Give an example of a non-holonomic constraint. b) Five identical flat circular plates are served on a circular conveyor belt. The plates have mass m, radius 5 cm and moment of inertia Ip about their axis of symmetry. They are free to move under gravity on top of a conveyor belt which has inner radius a, outer radius b and moment of inertia Ic about a vertical axis through its centre. From above, it looks like the diagram below. a The belt is banked at a fixed angle a such that the inner edge is lower than the outer edge. Assuming the conveyor belt rotates freely, how many degrees of freedom does this system have? Find the Lagrangian for the system. Hence find and identify any conserved quanti- ties of the system. 1 1arrow_forward
- A ring (mass 2 M, radius 2 R) rotates in a CCW direction with an initial angular speed 1 ω. A disk (mass 4 M, radius 1 R) rotates in a CW direction with initial angular speed 4 ω. 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 Li of the ring+disk system? Write your answer in terms of MR2ω. What is the final angular velocity ωf of the ring+disk system? Write your answer in terms of ω.arrow_forwardDetermine the angular momentum of a 78-g particle about the origin of coordinates when the particle is at x = 4.9 m, y = -6.3 m, and it has velocity v = (3.51-80k) m/s. Find the x-component. Express your answer using two significant figures. Lx = ΜΕ ΑΣΦ Submit Request Answer ▼ Part B Find the y-component. Express your answer using two significant figures. Ly= ΜΕ ΑΣΦ Submit Request Answer Part C Find the z-component. Express your answer using two significant figures. ? kg-m²/s ? kg-m²/sarrow_forwardEngineering Dynamics need help from 4,5,6,7 thank you A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning