An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s². What is the tangential speed of a point on the rim of the turntable at t = 0.200 s?

Verified step by step guidance

1. Convert the given angular velocity and angular acceleration from revolutions per second (rev/s) and revolutions per second squared (rev/s²) to radians per second (rad/s) and radians per second squared (rad/s²), respectively. Use the conversion factor: 1 revolution = 2π radians.
2. Calculate the angular velocity (ω) at time t = 0.200 s using the formula for angular velocity under constant angular acceleration: $\omega =\omega o_{}+\alpha t$, where $\omega o_{}$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $t$ is the time.
3. Determine the radius of the turntable from its diameter. The radius is half the diameter: $r=\frac{0.750}{2}=0.375m$.
4. Use the relationship between tangential speed (v) and angular velocity (ω): $v=r\omega$, where $r$ is the radius and $\omega$ is the angular velocity at t = 0.200 s.
5. Substitute the values of $r$ and $\omega$ into the formula for tangential speed to find the result: $v=0.375\cdot \omega$.

Key Concepts

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around an axis, expressed in radians per second or revolutions per second. In this scenario, the initial angular velocity of the turntable is given as 0.250 rev/s, indicating the rate of rotation at the start of the observation.

Angular Acceleration

Angular acceleration refers to the rate of change of angular velocity over time, typically measured in revolutions per second squared. In this case, the turntable has a constant angular acceleration of 0.900 rev/s², which means its rotational speed increases steadily as time progresses.

Tangential Speed

Tangential speed is the linear speed of a point on the circumference of a rotating object, calculated as the product of the angular velocity and the radius of the rotation. For the turntable, the tangential speed at any moment can be determined using the formula v = r * ω, where r is the radius and ω is the angular velocity at that time.