Equations of Rotational Motion Video Lessons

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Problem: A wheel is rotating about an axis that is in the z-direction. The angular velocity z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at exttip{t}{t} = 12.0 s . We have taken counterclockwise rotation to be positive.(a) Is the angular acceleration during this time interval positive or negative?(b) How long is the time interval during which the speed of the wheel is increasing?(c) How long is the time interval during which the speed of the wheel is decreasing?(d) What is the angular displacement of the wheel from t = 0 s to exttip{t}{t} = 12.0 s ?

FREE Expert Solution

This a rotational kinematics problem since we have an acceleration. We'll need the rotational kinematics equations. 

Rotational kinematic equations:

ωf=ω0 + αtθ=12(ω0+ωf)tθ=ω0t +12αt2ωf2=ω02+2αθ

(a) the angular velocity changes from -6.00 rad/s to +4.00 rad/s. This means that the angular acceleration should be positive because the angular velocity is becoming more positive. 

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Problem Details

A wheel is rotating about an axis that is in the z-direction. The angular velocity z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at = 12.0 s . We have taken counterclockwise rotation to be positive.

(a) Is the angular acceleration during this time interval positive or negative?

(b) How long is the time interval during which the speed of the wheel is increasing?

(c) How long is the time interval during which the speed of the wheel is decreasing?

(d) What is the angular displacement of the wheel from t = 0 s to = 12.0 s ?

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