To solve this problem, we'll need to use some formulas related to rotational motion. Let's go through the calculations step by step:
(a) Angular acceleration:
We know that angular acceleration (αalphaα) is the rate at which angular velocity (ωomegaω) changes over time. In this case, we're given the initial angular velocity (ω0omega_0ω0), final angular velocity (ωfomega_fωf), and the time interval (ttt).
Given: Initial angular velocity, ω0omega_0ω0 = 120 rpm (revolutions per minute) Final angular velocity, ωfomega_fωf = 0 (since the wheel comes to rest) Time interval, ttt = 1 minute = 60 seconds
First, let's convert the initial angular velocity from rpm to radians per second (rad/s): ω0=120 rpm×2π60 rad/s=4π rad/somega_0 = 120 , ext{rpm} imes frac{2pi}{60} , ext{rad/s} = 4pi , ext{rad/s}ω0=120rpm×602πrad/s=4πrad/s
Now we can calculate the angular acceleration using the formula: α=ΔωΔtalpha = frac{Deltaomega}{Delta t}α=ΔtΔω</sp