Answered: At time t=0 a grinding wheel has an…

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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Question

At time t=0 a grinding wheel has an angular velocity of 27.0 rad/s . It has a constant angular acceleration of 34.0 rad/s^2until a circuit breaker trips at time t= 2.20 s . From then on, the wheel turns through an angle of 438 rad as it coasts to a stop at constant angular deceleration.

a) Through what total angle did the wheel turn between t=0 and the time it stopped? Express your answer in radians.

b) At what time does the wheel stop?

Express your answer in seconds.

What was the wheel's angular acceleration as it slowed down?

Express your answer in radians per second^2.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Expert Solution

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$I n i t i a l a n g u l a r v e l o c i t y (ω_{o}) = 27 \frac{r a d}{s e c} a n g u l a r a c c e l e r a t i o n f o r f i r s t 2.20 s e c o n d s (α_{1}) = 34 \frac{r a d}{s^{2}} a n g u l a r d i p l a c e m e n t a f t e r 2.20 s e c o n d s = 438 r a d f i n a l a n g u l a r v e l o c i t y = 0 \frac{r a d}{s}$

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