Angular Velocity and Acceleration in Rotating Wheel

What is the angular velocity of a wheel with a radius of 10cm rotating at 3.14rad/s?

a. Calculate the linear velocity of the wheel.

b. Determine the tangential velocity, tangential acceleration, normal acceleration, and total acceleration of a point on the rim of the wheel.

Answer:

The angular velocity of the wheel is 3.14 rad/s. The linear velocity is 0.314 m/s. The tangential velocity, tangential acceleration, normal acceleration, and total acceleration of a point on the rim of the wheel can be calculated using the given formulas.

The angular velocity of a wheel is given by the formula ω = αt, where ω is the angular velocity, α is the angular acceleration, and t is the time. In this case, the angular acceleration is 3.14 rad/s and the time is 1 second, so the angular velocity is 3.14 rad/s.

To find the linear velocity, we can use the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel. In this case, the radius is 10 cm (0.1 m), so the linear velocity is (3.14 rad/s)(0.1 m) = 0.314 m/s.

The tangential velocity, tangential acceleration, normal acceleration, and total acceleration of a point on the rim of the wheel can be calculated using the formulas:

v = ωr,

at = αr,

an = v²/r, and

atotal = √(at² + an²).