Question

The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy plane is given by \(\vec{P}(t) = A \cos(\omega t) \hat{i} + A \sin(\omega t) \hat{j}\). The distance from the axis is \(A = 2.50\text{ m}\) and \(\omega = 0.550 \text{ rad/s}\). The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy plane is given by \(\vec{P}(t) = A \cos(\omega t) \hat{i} + A \sin(\omega t) \hat{j}\). The distance from the axis is \(A = 5.0\text{ m}\) and \(\omega = 0.89 \frac{rad}{s}\). What is its velocity at \(t = 10\text{s}\)? a) What is the position of the particle at \(t = 19.0\text{ s}\)? \(\vec{P}(t = 19.0\text{ s}) = -1.375\text{m} \hat{i} + -4.33\text{m} \hat{j}\) b) What is the velocity of the particle at \(t = 19.0\text{ s}\)? \(\vec{v}(t = 19.0\text{ s}) = 4.27\text{m/s} \hat{i} + -1.375\text{m/s} \hat{j}\) c) What is the acceleration of the particle at \(t = 19.0\text{ s}\)? \(\vec{a}(t = 19.0\text{ s}) = 1.09\text{m/s}^2 \hat{i} + 1.31\text{m/s}^2 \hat{j}\) d) What is the magnitude of the tangential acceleration of the particle at \(t = 19.0\text{ s}\)? \(|\vec{a}_t(t = 19.0\text{ s})| = 0\text{m/s}^2\) e) What is the centripetal acceleration of the particle at \(t = 19.0\text{ s}\)? \(\vec{a}_c(t = 19.0\text{ s}) = 1.51\text{m/s}^2 \hat{i}\)

          The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy
plane is given by \(\vec{P}(t) = A \cos(\omega t) \hat{i} + A \sin(\omega t) \hat{j}\). The distance from the axis is \(A = 2.50\text{ m}\) and
\(\omega = 0.550 \text{ rad/s}\).
The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy
plane is given by \(\vec{P}(t) = A \cos(\omega t) \hat{i} + A \sin(\omega t) \hat{j}\). The distance from the axis is \(A = 5.0\text{ m}\) and
\(\omega = 0.89 \frac{rad}{s}\). What is its velocity at \(t = 10\text{s}\)?
a) What is the position of the particle at \(t = 19.0\text{ s}\)?
\(\vec{P}(t = 19.0\text{ s}) = -1.375\text{m} \hat{i} + -4.33\text{m} \hat{j}\)
b) What is the velocity of the particle at \(t = 19.0\text{ s}\)?
\(\vec{v}(t = 19.0\text{ s}) = 4.27\text{m/s} \hat{i} + -1.375\text{m/s} \hat{j}\)
c) What is the acceleration of the particle at \(t = 19.0\text{ s}\)?
\(\vec{a}(t = 19.0\text{ s}) = 1.09\text{m/s}^2 \hat{i} + 1.31\text{m/s}^2 \hat{j}\)
d) What is the magnitude of the tangential acceleration of the particle at \(t = 19.0\text{ s}\)?
\(|\vec{a}_t(t = 19.0\text{ s})| = 0\text{m/s}^2\)
e) What is the centripetal acceleration of the particle at \(t = 19.0\text{ s}\)?
\(\vec{a}_c(t = 19.0\text{ s}) = 1.51\text{m/s}^2 \hat{i}\)

The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy
plane is given by P⃗(t) = A cos(ω t) î + A sin(ω t) ĵ. The distance from the axis is A = 2.50 m and
ω = 0.550 rad/s.
The position of a particle rotating at uniform circular motion in the counterclockwise direction in the xy
plane is given by P⃗(t) = A cos(ω t) î + A sin(ω t) ĵ. The distance from the axis is A = 5.0 m and
ω = 0.89 (rad)/(s). What is its velocity at t = 10s?
a) What is the position of the particle at t = 19.0 s?
P⃗(t = 19.0 s) = -1.375mî + -4.33mĵ
b) What is the velocity of the particle at t = 19.0 s?
v⃗(t = 19.0 s) = 4.27m/sî + -1.375m/sĵ
c) What is the acceleration of the particle at t = 19.0 s?
a⃗(t = 19.0 s) = 1.09m/s^2 î + 1.31m/s^2 ĵ
d) What is the magnitude of the tangential acceleration of the particle at t = 19.0 s?
|a⃗t(t = 19.0 s)| = 0m/s^2
e) What is the centripetal acceleration of the particle at t = 19.0 s?
a⃗c(t = 19.0 s) = 1.51m/s^2 î

Added by Adam R.

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