Angular Position, Velocity, and Acceleration in Fixed-Axis Rotation

All flashcards

Angular displacement

The change in angular position, calculated as final angular position minus initial angular position.

Average angular velocity

Angular displacement divided by the elapsed time: $\bar{\omega}=\Delta\theta/\Delta t$.

Angular velocity vector

A vector directed along the rotation axis, with direction given by the right-hand rule.

Tangential velocity

The velocity of a point on a rotating body, given by $\vec{v}=\vec{\omega}\times\vec{r}$.

Tangential acceleration

The acceleration component that changes tangential speed; for fixed-axis rotation, $\vec{a}_t=\vec{\alpha}\times\vec{r}$.

Quiz questions

1. A wheel's angular position changes by $12\,\text{rad}$ in $3\,\text{s}$. What is its average angular velocity?Answer: $4\,\text{rad/s}$
2. A point is $0.30\,\text{m}$ from a rotation axis, and the body rotates at $5.0\,\text{rad/s}$. What is the point's tangential speed?Answer: $1.5\,\text{m/s}$
3. Viewed on a page, a wheel rotates counterclockwise. Which direction does its angular-velocity vector point?Answer: Out of the page
4. A rotating object has angular velocity and angular acceleration directed along the same axis direction. What happens to its rotational rate?Answer: Its angular speed increases.
5. A rotor turns at $120\,\text{rev/min}$. What is this rate in radians per second?Answer: $4\pi\,\text{rad/s}$