A potter’s wheel moves from rest to an angular speed of 0.30 rev/s in 25.8 s.
Assuming constant angular acceleration,
what is its angular acceleration in rad/s2
?
Answer in units of rad/s^2
Hey, this is so close to your earlier problems that I am getting worried. Better review the chapter !
anyway
0.30 revs is how many radians?
multiply by 2 pi
0.30 revs * 2 pi radians/rev = 1.88 radians
so it goes from 0 to 1.88 radians/second in 25.8 seconds
acceleration = change in velocity / change in time
= 1.88 rad/s / 25.8 s = (1.88/25.8) rad/s^2
Yeah thank you and yeah i need to study
To find the angular acceleration, we can use the formula:
\( \text{{Final angular speed}} = \text{{Initial angular speed}} + \text{{Angular acceleration}} \times \text{{time}} \)
Given:
\( \text{{Final angular speed}} = 0.30 \) rev/s
\( \text{{Initial angular speed}} = 0 \) rev/s (since it starts from rest)
\( \text{{time}} = 25.8 \) s
First, let's convert the rev/s values to rad/s:
1 revolution (rev) = \( 2\pi \) radians (rad)
Therefore, \( 0.30 \) rev/s = \( 0.30 \times 2\pi \) rad/s = \( 0.60\pi \) rad/s
Substituting these values into the formula, we have:
\( 0.60\pi \) rad/s = \( 0 \) rad/s + \( \text{{Angular acceleration}} \times 25.8 \) s
To isolate the angular acceleration, we can rearrange the equation:
\( \text{{Angular acceleration}} = \frac{{0.60\pi \, \text{{rad/s}} - 0 \, \text{{rad/s}}}}{{25.8 \, \text{{s}}}} \)
Simplifying the equation:
\( \text{{Angular acceleration}} = \frac{{0.60\pi}}{{25.8}} \) rad/s²
Calculating the value:
\( \text{{Angular acceleration}} = 0.0733 \, \text{{rad/s}}^2 \)
Therefore, the angular acceleration of the potter's wheel is \( 0.0733 \, \text{{rad/s}}^2 \) (rounded to four decimal places).