A grinding wheel starts from rest and spins with constant angular acceleration. If it takes 2.0 s for it to make the first complete revolution, a) What is the constant angular acceleration? b) What is the total angular displacement in 4.0 s starting from rest?

A grinding wheel starts from rest and spins with constant angular acceleration. If it takes 2.0 s for it to make the first complete revolution, a) What is the constant angular acceleration? b) What is the total angular displacement in 4.0 s starting from rest?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 4P

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

A grinding wheel starts from rest and spins with constant angular acceleration. If it takes
2.0 s for it to make the first complete revolution,
a) What is the constant angular acceleration?
b) What is the total angular displacement in 4.0 s starting from rest?
a, = constant
WOz
azt
0 = 00 + wozt + at
WOz
2a,(0 – 60)
0 – 0o = (@oz + w;)t

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