**Problem Statement:**2. The figure shows a uniform disk that can rotate around a fixed axis through its center, perpendicular to the page. The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. At time \( t = 0 \), two forces are applied tangentially to the rim as indicated. The force \( \vec{F}_1 \) has a magnitude of 0.1 N, and the force \( \vec{F}_2 \) has a magnitude of 0.15 N.**Diagram Explanation:**The diagram illustrates a top view of the disk with vectors representing the forces. The disk's center is marked with a small black dot. \( \vec{F}_1 \) is directed horizontally to the right and tangential to the disk at an angle, while \( \vec{F}_2 \) is directed downward and tangential to the rim. The coordinate axes \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are shown next to the disk.**Questions:**(a) Indicate the directions (\( \pm \hat{k} \)) of the following:- \( \vec{\tau}_1 \), the torque due to \( \vec{F}_1 \)- \( \vec{\tau}_2 \), the torque due to \( \vec{F}_2 \)- \( \vec{\alpha} \), the angular acceleration after the disk starts rotating.- \( \vec{\omega} \), the angular velocity after the disk starts rotating.(b) What is the angular momentum \( \vec{L} \) of the disk after the forces at \( t = 10 \, \text{s} \)?*Note: The moment of inertia for a uniform disk is \( I = \frac{1}{2} MR^2 \).*

Given Data The radius of the disk (R)=0.02m Mass of the disk(m) =0.02kg The force F1 has a magnitude of (F1) = 0.1N The force F2 has a magnitude of (F2) = 0.15N The moment of inertia of the uniform disk is (I) = 12MR2 Definition of Torque: Torque is a measure force that can cause an object to rotate about an axis. Torque causes an object to acquire angular acceleration.So, the torque is a vector quantity, the direction of the torque depends on the direction of force on the axis. Torque τ=F×r From the right hand grip rule, if the hand is curled around the axis of rotation with the fingers pointing in the direction of force then the torque vector points in the direction of thumb.a) The torque due to F1 is τ1 =R×F1=RF1sin90o=0.02×0.1=0.002N.m From the right hand grip rule we can say that the torque is into of the page -k^ The torque due to F2 is τ2=R×F2 =RF2sin90o=0.02×0.15=0.003N.m the direction of torque due to F2 is out of the page +k^ So, the total torque is τ=τ2-τ1 =0.003-0.002 =0.001N.m From the above torques due F1 and F2 , the torque due to F2 is more than F1 . Therefore the net torque will be in the direction of F2 The angular acceleration is given by τ=Iα α=τI=τ12MR2=0.0010.5×0.02×0.022=250rad/s2 The angular acceleration will be similar to the torque that will be out the page +k^ The angular velocity after the disk starts rotating is ω=αt. it will be out of the page similar to angular acceleration +k^ b) The angular momentum of the L of the disk after forces at 10s is We know that initial angular speed is zero after 10s the final angular speed is ω=ωo+αt=0+250×10=2500rad/s Now the angular momentum is given by L=Iω=12MR2ω=0.5×0.02×0.022×2500=0.01kg.m2/sec

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Physics

2. The figure at the right shows a uniform disk that can rotate around a fixed axis through its center. (The axis is perpendic- ular to the page.) The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. Starting at time t = 0, two forces are applied tangentially to the rim as indicated. The force F₁ has a magnitude of 0.1 N, and the force F₂ has a magnitude of 0.15 N. TE ☐ k KO (.m Î

2. The figure at the right shows a uniform disk that can rotate around a fixed axis through its center. (The axis is perpendic- ular to the page.) The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. Starting at time t = 0, two forces are applied tangentially to the rim as indicated. The force F₁ has a magnitude of 0.1 N, and the force F₂ has a magnitude of 0.15 N. TE ☐ k KO (.m Î

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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