Question

The wheel of a car has a radius 20cm . It initially rotates at 120rpm . A minute later, it makes 90 revolutions . (a) What is the angular acceleration of the wheel? (b) How far does the car travel before coming to rest?

Answer 1

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 ($\alpha$) is the rate at which angular velocity ($\omega$) changes over time. In this case, we're given the initial angular velocity (${\omega }_0$), final angular velocity (${\omega }_f$), and the time interval ($t$).

Given: Initial angular velocity, ${\omega }_0$ = 120 rpm (revolutions per minute) Final angular velocity, ${\omega }_f$ = 0 (since the wheel comes to rest) Time interval, $t$ = 1 minute = 60 seconds

First, let's convert the initial angular velocity from rpm to radians per second (rad/s): ${\omega }_0=120\text{rpm}\times \frac{2\pi }{60}\text{rad/s}=4\pi \text{rad/s}$

Now we can calculate the angular acceleration using the formula: α=ΔωΔtalpha = frac{Deltaomega}{Delta t}α=ΔtΔω</sp