Question

A motorized wheel is spinning with a rotational velocity of w0 = 1.25 rad/s. At t=0s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by:

a) w(t) = 1.25 rad/s
b) w(t) = 2.50 rad/s
c) w(t) = 0.625 rad/s
d) The new rotational velocity equation is not provided.

Answer 1

Physics questions here address the dynamics of rotational motion including angular velocity, acceleration, and their conversion to linear motion. They cover the application of formulas relating rotational and linear quantities, and the investigation of scenarios involving rotating wheels and car tires.

Step-by-step explanation:

The subject of these questions is Physics, particularly focusing on the concepts of angular velocity, angular acceleration, and their relationship to linear velocity. In Physics, we often deal with problems involving rotational motion and how it translates to linear motion, typically using radial distances for conversion.

For instance, to calculate the final angular velocity given a constant angular acceleration, one can use the formula ω = ω0 + αt, where ω0 is the initial angular velocity, α is angular acceleration, and t is time.

Similarly, the linear velocity v of a point on a rotating object is related to its angular velocity ω and radius r through the equation v = rω. These relationships are essential in many practical applications, such as determining the speed of a car's tire based on the angular velocity and tire radius.

To answer question 42, we must use the formula for rotational motion θ = θ0 + ω0t + 0.5αt², where θ is the angular displacement, θ0 the initial angular displacement, and ω0 the initial angular velocity (zero in this case since the wheel starts from rest).

For the linear acceleration of a point on the edge of the wheel, you apply the formula ar = rα, where ar is the linear acceleration.