9 - Rotational Motion and Dynamics Free Online FlashCards

What does angular position describe?

Angular position describes an object's orientation relative to a chosen reference direction and is represented by $\theta$.

How many radians are in one revolution?

One revolution equals $2\pi$ radians, or $360^\circ$.

What equation gives arc length during rotation?

The arc length is $s=r\theta$, where $\theta$ must be measured in radians.

How are tangential speed and angular velocity related?

For a point at radius $r$, tangential speed is $v_t=r\omega$. Points farther from the axis move faster tangentially.

How does the right-hand rule determine angular velocity direction?

The right-hand rule gives the direction: curl your fingers in the rotation direction; your thumb points along $\vec{\omega}$.

How do tangential and centripetal acceleration differ?

Tangential acceleration changes a point's speed, while centripetal acceleration changes the direction of its velocity toward the axis.

Does positive angular acceleration always mean speeding up?

A positive angular acceleration means angular velocity becomes more positive; it does not necessarily mean the object speeds up.

What is the general formula for torque magnitude?

Torque magnitude is $\tau=rF\sin\phi$, where $\phi$ is the angle between the position vector and force.

What is the lever arm?

The lever arm is the perpendicular distance from the axis to the force's line of action.

Why are torque and energy different despite sharing units?

Torque and energy both have units of $\text{N}\cdot\text{m}$, but torque causes angular acceleration while energy measures the capacity to do work.

How is rotational inertia calculated for point masses?

For point masses, rotational inertia is $I=\sum_i m_i r_i^2$. Mass farther from the axis contributes disproportionately because distance is squared.

What is the rotational inertia of a solid disk about its center?

A solid disk or cylinder rotating about its center has $I=\frac{1}{2}MR^2$.