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tem_osu

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**[SOLVED] Rotational Kinematics**

## Homework Statement

A person is riding a bicycle, and its wheels have an angular velocity of +18.0 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is +13.5 revolutions.

(a) How much time does it take for the bike to come to rest?

(b) What is the angular acceleration of each wheel?

## Homework Equations

(a) θ = (ω

*0*+ ω)t

(b) ω = ω

*0*+ αt

## The Attempt at a Solution

(a) +13.5 rev = (18.0 rad/s - 0 rad/s)t

t = (+13.5 rev)/(18.0 rad/s) = 0.75 - wrong answer

(b) (ω - ω

*0*)/t = α

(0 rad/s - 18.0 rad/s)/0.75 = α - wrong answer

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## Homework Statement

After 10.0 s, a spinning roulette wheel at a casino has slowed down to an angular velocity of +1.70 rad/s. During this time, the wheel has an angular acceleration of -5.05 rad/s^2. Determine the angular displacement of the wheel.

## Homework Equations

ω^2 = ω

*0*^2 + 2α(θ − θ

*0*)

## The Attempt at a Solution

(+1.70 rad/s)^2 = 0 + 2(-5.05 rad/s^2)θ

θ = [(1.70 rad/s)^2]/2(-5.05 rad/s^2) = -0.286 - wrong answer

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Please help me, I don't know what I'm doing wrong.