Answered: "A rotating wheel's rim's point's angular position is..."

High School
Physics
Force, Motion and Energy
Acceleration Due to Gravity

kyrtilioo

Answered question

2022-12-16

A rotating wheel's rim's point's angular position is determined by

θ = 4 t - 3 t^{2} + t^{3}

, where

θ

is in radians and t is in seconds. What is the instantaneous angular acceleration at

t = 2

sec?
1)

4 r a d / s^{2}

2 r a d / s^{2}

<br.3)

6 r a d / s^{2}

3 r a d / s^{2}

Answer & Explanation

Braylon Ochoa

Beginner2022-12-17Added 4 answers

The correct option is D

6 r a d / s^{2}

Given,

θ = 4 t - 3 t^{2} + t^{3}

ω = \frac{d θ}{d t} a n d a = \frac{d ω}{d t}

\Rightarrow ω = \frac{d θ}{d t} = 4 - 6 t + 3 t^{2}

a n d α = \frac{d ω}{d t} = \frac{d}{d t} (4 - 6 t + 3 t^{2})

= - 6 + 6 t

t = 2 s, α = - 6 + 6 \times 2

= 6 r a d / s^{2}

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