Question

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?

Answer 1

Answer:$a_{t}=3.96$

$a_{c}=0.8712$

Explanation:

Given

$\theta =0.220e^{3t}$

r=2cm

Now angular velocity is given by $\omega =\frac{\mathrm{d}\theta}{\mathrm{d}t}$

$\omega =0.66e^{3t}$

Now linear velocity(v) is given =$\omega r$

$v=1.32e^{3t}$

Now tangential component of acceleration is given by

$a_{t}=\frac{\mathrm{d}\vec{v}}{\mathrm{d}t}=3.96e^{3t}$

at t=0

$a_{t}=3.96cm/s^2$

radial component of acceleration is given by

$a_{c}=\omega ^{2}r$

$a_{c}=0.4356e^{6t}\times 2$

$a_{c}=0.8712e^{6t} cm/s^{2}$

at t=0

$a_c=0.8712 cm/s^{2}$