Rotational Equilibrium and Newton's First Law - AP Physics C: Mechanics

Decreases angular acceleration for the same torque. Higher inertia requires more torque for same acceleration.

Further mass distribution from the axis increases inertia. Mass farther from axis increases resistance to rotation.

$I = \frac{1}{2} m r^2$. Half the value for solid cylinder compared to hoop.

A change in angular velocity. Net torque produces angular acceleration.

The point where the mass of a system is concentrated. Balance point where total mass appears concentrated.

$\tau = 0.4 \times 50 \times \text{sin}(45) = 14.14 \text{Nm}$. Use $\tau = rF\sin\theta$ with $45°$ angle.

Yes, it is in rotational equilibrium. Equal opposing torques cancel for zero net torque.

Magnitude of force, distance from pivot, angle of force. All three determine the rotational effect.

The velocity of the object. Inertia depends on mass and distance, not velocity.

$\tau_{net} = 5 \times 0.2 - 5 \times 0.3 = -0.5 \text{Nm}$. Subtract opposing torques to find net effect.

Torque is the rotational equivalent of force, $\tau = r \times F$. Force applied at a distance creates rotational tendency.

An object will not rotate or will rotate at constant angular velocity unless acted upon by a net torque. Objects maintain their rotational state unless disturbed by torque.

$\tau$ represents torque. Greek letter tau denotes rotational force.

The sum of clockwise torques equals the sum of counterclockwise torques. Balanced moments create no net rotation.

If no net external torque acts on a system, its angular momentum is conserved. No external torque means angular momentum stays constant.

The velocity of the object. Inertia depends on mass and distance, not velocity.

$\tau = 0.3 \times 20 \times \text{sin}(90) = 6 \text{Nm}$. Perpendicular force gives maximum torque.

$\tau = \textbf{r} \times \textbf{F}$. Cross product of position and force vectors.

The object is in rotational equilibrium. No net torque means no angular acceleration.

Determines the torque produced by the force. Force direction affects torque magnitude and direction.

The point where the mass of a system is concentrated. Balance point where total mass appears concentrated.

Sum of clockwise moments equals sum of counterclockwise moments for equilibrium. Fundamental rule for rotational equilibrium.

$I = \frac{1}{12} m L^2$. Inertia formula for rod rotating about its center.

$\tau_{net} = 5 \times 0.2 - 5 \times 0.3 = -0.5 \text{Nm}$. Subtract opposing torques to find net effect.

Torque is the rotational equivalent of force, $\tau = r \times F$. Force applied at a distance creates rotational tendency.

The unit of torque is the Newton-meter (Nm). Force times distance gives units of $N \cdot m$.

$I = m r^2$. All mass is at distance $r$ from the center.

The object remains in its current state of rotational motion. No torque means constant angular velocity.

Torque is the rotational effect of a force, $\tau = r \times F \times \text{sin}(\theta)$. Torque is force creating rotation about a pivot.