Question

A potter’s wheel moves from rest to an angular speed of 0.50 rev/s in 28.9 s. Assuming constant angular acceleration, what is its angular acceleration in rad/s2 ? Answer in units of rad/s 2 .

Answer 1

The angular acceleration of the potter's wheel is 0.109 rad/s².

Step-by-step explanation:

The formula to calculate angular acceleration is:

angular acceleration (α) = ωf - ωi / t

Where:

ωf is the final angular velocity

ωi is the initial angular velocity

t is the time taken to reach the final angular velocity

In this case, the initial angular velocity (ωi) is 0 (as the wheel starts from rest), the final angular velocity (ωf) is 0.50 rev/s, and the time (t) is 28.9 s. Substituting these values into the formula:

α = 0.50 rev/s - 0 / 28.9 s = 0.50 rev/s / 28.9 s = 0.0173 rev/s²

To convert rev/s² to rad/s², we multiply by 2π (since 1 revolution = 2π radians):

α = 0.0173 rev/s² × 2π rad/rev = 0.109 rad/s²

Therefore, the angular acceleration of the potter's wheel is 0.109 rad/s².

Answer 2

0.108 rad/s².

Step-by-step explanation:

Given that

Initial angular velocity ,ωi = 0 rad/s

Final angular velocity ωf= 0.5 rev/s

We know that

1 rev/s = 6.28 rad/s

ωf= 3.14 rad/s

t= 28.9 s

We know that (if acceleration is constant)

ωf=ωi + α t

α=Angular acceleration

3.14 = 0 + α x 28.9

`\alpha=(3.14)/(28.9)\ rad/s^2\\\alpha=0.108\ rad/s^2`

Therefore the acceleration will be 0.108 rad/s².

Therefore the answer will be 0.108 rad/s².