Question

A record on a turntable is spinning and slowing down. At t=0s, the angular velocity of the record is 20.0ra(d)/(s) with a constant acceleration of -5.0ra(d)/(s²). How long does it take for the record to come to rest?

Answer 1

To determine the time it takes for the turntable to stop, the rotational kinematic equation (ω = ω0 + αt) is used, with ω0 being the initial angular velocity of 20.0 rad/s and α the angular acceleration of -5.0 rad/s2. Solving for the time (t) reveals that the turntable will stop after 4.0 seconds.

Step-by-step explanation:

The aim of this problem is to determine how long it takes for a turntable to stop when it experiences a negative angular acceleration. We know that angular velocity (ω) decreases due to angular acceleration (α), causing the turntable to come to rest. To find the time (t) it takes for the turntable to stop, we can use the rotational kinematic equation: ω = ω0 + αt, where ω0 is the initial angular velocity and α is the angular acceleration.

Given the initial angular velocity ω0 = 20.0 rad/s and the angular acceleration α = -5.0 rad/s2, we can set the final angular velocity ω to 0 because the turntable comes to rest, and solve for t:

0 = 20.0 rad/s + (-5.0 rad/s2)t

0 = 20.0 - 5.0t

t = 20.0 / 5.0

t = 4.0 s

The turntable will come to rest after 4.0 seconds.