Question

A potter's wheel is spinning with an initial angular velocity of 18 rad/s . It rotates through an angle of 60.0 rad in the process of coming to rest.What was the angular acceleration of the wheel? How long does it take for it to come to rest?

Answer 1

We can use the following kinematic equations to find the angular acceleration and time it takes for the wheel to come to a stop:

θ = θ_0 + ω_0 t + 1/2 α t^2

ω^2 = ω_0^2 + 2 α (θ - θ_0)

where:

θ = final angle = 60.0 rad
θ_0 = initial angle = 0
ω_0 = initial angular velocity = 18 rad/s
α = angular acceleration (unknown)
t = time it takes for the wheel to come to rest (unknown)

Using the second equation, we can solve for α:

α = (ω^2 - ω_0^2) / 2(θ - θ_0)
= (0 - (18 rad/s)^2) / 2(60.0 rad - 0)
= -2.7 rad/s^2

Therefore, the angular acceleration of the wheel is -2.7 rad/s^2 (negative sign indicates deceleration).

Using the first equation, we can solve for t:

θ = θ_0 + ω_0 t + 1/2 α t^2
60.0 rad = 0 + (18 rad/s) t + 1/2 (-2.7 rad/s^2) t^2

Solving for t using the quadratic formula, we get:

t = 6.57 s

Therefore, it takes 6.57 seconds for the wheel to come to rest.