Final answer:
To find the time for a record player with an angular acceleration of 0.5 rad/s^2 to complete 2 revolutions, we use the kinematic equation for rotational motion. The record player takes 4π seconds to complete 2 revolutions.
Step-by-step explanation:
The student is asking about the time it will take for a record player with an angular acceleration of 0.5 rad/s2 to undergo 2 complete revolutions. To solve this, we can use the kinematic equation for rotational motion, θ = ω0t + 0.5αt2, where θ is the angular displacement in radians, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.
Since the record player starts from rest, ω0 = 0. Two complete revolutions mean the angular displacement θ = 2 × 2π radians (because one complete revolution is 2π radians). Plugging in the values we get:
4π = 0.5 × 0.5t24π = 0.25t2= × 16πt = 4π s
Therefore, the record player takes 4π seconds to complete 2 revolutions.