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Problem: The angular position of a point on the rim of a rotating wheel is given by θ = 4.0  t — 3.0t2 + t3, where θ is in radians and t is in seconds. What are the angular velocities at:(a) t = 2.0 s and (b) t = 4.0 s? c) What is the average angular acceleration for the time interval that begins at  t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at: (d) the beginning and (e) the end of this time interval?

FREE Expert Solution

Angular velocity is given by:

ω=dθdt

Average angular acceleration is expresed as:

αavg=ωt

Instantaneous angular acceleration:

α=dωdt

(a)

Angular velocity is:

ω=d(4.0t-3.0t2+t3)dt=4.0-6.0t+3t2

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Problem Details

The angular position of a point on the rim of a rotating wheel is given by θ = 4.0  t — 3.0t2 + t3, where θ is in radians and t is in seconds. What are the angular velocities at:

(a) t = 2.0 s and 

(b) t = 4.0 s? 

c) What is the average angular acceleration for the time interval that begins at  t = 2.0 s and ends at t = 4.0 s?

 What are the instantaneous angular accelerations at:

 (d) the beginning and 

(e) the end of this time interval?

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Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.