Question

a bicyclist starts from rest and begins riding down the street. after her wheels have rotated through ten revolutions, they have acquired an angular velocity of 12 rad/s rad/s . determine the angular acceleration of her wheels. express your answer in radians per second squared.

Answer 1

To determine the angular acceleration of the bicycle's wheels, you can use the formula for angular acceleration and plug in the given values.

Step-by-step explanation:

To determine the angular acceleration of the bicycle's wheels, we need to use the formula:

angular acceleration = ( final angular velocity - initial angular velocity ) / time

Given that the wheels have rotated through ten revolutions (or 20π radians), and the final angular velocity is 12 rad/s, we can plug these values into the formula:

angular acceleration = ( 12 rad/s - 0 rad/s ) / ( 20π radians )

Simplifying this expression will give us the angular acceleration in radians per second squared.

Answer 2

The angular acceleration of the bicycle wheels is 1.2 rad/s². This was determined using the kinematic equations for rotational motion, with the given angular velocity and the fact that the wheels rotated through 10 revolutions.

Step-by-step explanation:

To determine the angular acceleration of the bicyclist's wheels, we can use the formula α = ω / t, where α is the angular acceleration, ω is the angular velocity, and t is the time it takes to reach that angular velocity. The angular velocity (ω) is given as 12 rad/s, but we need to determine the time (t). We know that the wheels made 10 revolutions to reach this angular velocity. Each revolution is 2π radians, so 10 revolutions correspond to 10 × 2π radians. Using the kinematic equation ω = ω_0 + αt, where ω_0 is the initial angular velocity (zero in this case, because the bicyclist starts from rest), we can rearrange to find t = (ω - ω_0) / α. Plugging in values gives us t = (12 rad/s) / α.

Next, we use the equation θ = ω_0t + 0.5αt² to solve for α, where θ is the total angular displacement (10 × 2π radians) and ω_0 is again zero. Substituting the expression for t from above and solving for α yields α = 2θ / t² = 2 × (10 × 2π rad) / t² = 2 × (20π rad) / (12 rad/s / α)².

After solving the quadratic equation for α, we find that the angular acceleration is 1.2 rad/s².