Question

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval, the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval

Answer 1

The wheel turns through -25 radians during the 5.0-second interval, representing a clockwise rotation of 25 radians.

Step-by-step explanation:

To find out how many radians the wheel turns through during the 5.0-second interval, we need to use the formula:

θ = ω0t + 0.5αt2

where θ is the angle (in radians), ω0 is the initial angular velocity, α is the angular acceleration, and t is the time interval.

Using the given values, we have:

θ = (20 rad/s)(5.0 s) + 0.5(-10 rad/s²)(5.0 s)2

θ = 100 rad + 0.5(-10 rad/s²)(25 s²)

θ = 100 rad - 125 rad

θ = -25 rad

Therefore, the wheel turns through -25 radians during the 5.0-second interval. Since negative values represent a change in direction, we can say that the wheel turns clockwise through 25 radians.