### Problem StatementA door stopper spring is flicked from its equilibrium position, and the angular velocity of the plastic end is given by the function:\[\omega(t) = 5e^{-0.2t} \sin(4t)\]1. **Find its angular acceleration function \( \alpha(t) \).**2. **Find its angular displacement function \( \theta(t) \), assuming \( \theta(0) = 0 \).**3. **If the rotational motion is confined to the xy plane, what is the direction of the acceleration at \( t=0 \)?**Justify your answers with your rationale and equations used.

The motion of a body around a fixed point or fixed axis is known as angular motion. It's the angle…

Answered: A door stopper spring is flicked from…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A projectile of mass m moves to the right with a speed vi (see figure below). The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision. The moment of inertia of a rod is I = Md² and the moment of inertia of a particle is I = mr². 12 a. What is w, the angular speed of the system after the collision. mdvi Md²+1md² 12 b. What is the kinetic energy before the collision? Answer: KE¡ = m(v¡)². c. What is the kinetic energy after the collision? (0₁)² Answer: W= 1 m²d² Answer: KE₁ = = =+M₁2² +² md² 12 4 m O d M O 3
A block with mass m = 5.00 kg slides down a surface inclined 36.9° to the horizontal (the figure (Figure 1)). The coefficient of kinetic friction is 0.27. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 16.0 kg and moment of inertia 0.500 kg · m? with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.250 m from that axis. Part A What is the acceleration of the block down the plane? Expresss your answer in meters per second squared. a = m/s? Part B What is the tension in the string? Express your answer in newtons. να ΑΣφ. T = Figure Provide Feedback 5.00 kg 36.9
• Problem 3.22 The potential energy between the atoms of an hydrogen molecule can be modelled by means of the Morse potential -2(r – ra) (r V (r) = V exp 2 еxp where Vo = 7 × 10 12 erg, ) = 8 x 10-º cm and a = 5 x 10-º em.
Determine the rate of change of the angular momentum HG of the disk of Prob. 18.8 for an arbitrary value of β, knowing that the disk has an angular velocity, knowing that the disk has an angular velocity w=w and an angular acceleration a = ai.
Express the answer without rounding off.
Let B be the solid bounded by the surfaces z = x^2+2y^2, x^2+y^2=16, and the xy-plane(distances in cm). If B has a constant mass density of 5g/cm^3, find the moment of inertia of B about the axis through(4,3,2) that is perpendicular to the yz-plane
The 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 B
An experimental device imparts a force of magnitude F = 59 lb to the front edge of the rim at A to simulate the effect of a slam dunk. Compute the moment of the force F about point O and about point B. The moments are positive if counterclockwise, negative if clockwise. Finally, locate a point C from the base at O to the location on the ground where the force imparts zero moment. The distance d from point O to point C is positive if C is to the right of O, and negative if to the left. Assume a = 36 in., b = 28 in., h = 12 in., H = 10 ft, c = 5, and d = 6. Answers: Mo= Mg = d = h i B -251.87 i-84.3 1.33 b lb-ft lb-ft ft
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