An object rotates about a fixed axis, and the angular position of a reference line on the object is given by θ = 0.220e3t, where θ is in radians and t is in seconds. Consider a point on the object that is 2.00 cm from the axis of rotation. At t = 0, what are the magnitudes of the point's (a) tangential component of acceleration and (b) radial component of acceleration?

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nuuk nuuk · Answer 1 · 2019-07-30T11:23:11+02:00

Answer:[tex]a_{t}=3.96[/tex]

[tex]a_{c}=0.8712[/tex]

Explanation:

Given

[tex]\theta =0.220e^{3t}[/tex]

r=2cm

Now angular velocity is given by [tex]\omega =\frac{\mathrm{d}\theta}{\mathrm{d}t}[/tex]

[tex]\omega =0.66e^{3t}[/tex]

Now linear velocity(v) is given =[tex]\omega r[/tex]

[tex]v=1.32e^{3t}[/tex]

Now tangential component of acceleration is given by

[tex]a_{t}=\frac{\mathrm{d}\vec{v}}{\mathrm{d}t}=3.96e^{3t}[/tex]

at t=0

[tex]a_{t}=3.96cm/s^2[/tex]

radial component of acceleration is given by

[tex]a_{c}=\omega ^{2}r[/tex]

[tex]a_{c}=0.4356e^{6t}\times 2[/tex]

[tex]a_{c}=0.8712e^{6t} cm/s^{2}[/tex]

at t=0

[tex]a_c=0.8712 cm/s^{2}[/tex]