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(I) An automobile engine slows down from 3500 rpm to 1200 rpm in 2.5 s. Calculate $(a)$ its angular acceleration, assumed constant, and $(b)$ the total number of revolutions the engine makes in this time.

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(a) $-96 \mathrm{rad} / \mathrm{s}^{2}$(b) 98 $\mathrm{rev}$

Physics 101 Mechanics

Chapter 10

Rotational Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Shy D.

October 4, 2020

Max S.

April 8, 2021

what is the angular displacment?

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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so here for part? A. When we want to find the angular acceleration, Alfa would be equal to the angular velocity final minus the angular velocity initial divided by T Aah! This would equal 1200 rpm's minus 3500 rpm's. This would be divided by tea or 2.5 seconds. Um, this is going to equal negative 2300 rpm's divided by again 2.5 seconds. And unless convert so this would be multiplied by two pi raid Ian's for everyone Revolution, and then we can multiply it by one minute for every 60 seconds. And this is giving us negative 96.3 radiance per second squared. So this would be your answer for a party for part B. We want to find the angular displacement during this time so the angular displacement can be found. Um, this would be equal to weaken, say Delta Theater. Rather, the change in angular displacement would be 1/2 times omega initial plus omega final multiplied by t. So essentially the average angular velocity multiplied by the time that the angular acceleration is being applied. So this would be equal to 1/2 um, well supplied by 3500 rpm plus 1200 rpm multiplied by 2.5 seconds. Delta Fada would then be equal to 1/2 times 4700 rpm, multiplied by 2.5 seconds, multiplied by one minute for every 60 seconds in order to convert. And this is giving us approximately 98 revolutions. This would be our answer for part B. That is the end of the solution. Thank you for watching.

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