AP Physics 1: Rotational Motion & Energy

ap physics 1: Rotational Motion & Energy. A high-tech physics illustration titled "ROTATIONAL MOTION & ENERGY" showing a spinning flywheel with symbols for angular displacement, velocity, and acceleration, plus the kinetic energy formula.

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AP Physics 1 Unit 7: Rotational Motion & Energy

Topics 7.2–7.3 (10–15% exam weight): In Part 1, we learned that Torque causes rotation. Now we analyze the motion itself. Replace linear variables with angular ones using radius ( $r$ ).

1. Linear ↔ Angular Bridge

Linear	Rotational	Bridge ( $r$ )
$x$ , $v$ , $a$	$\theta$ , $\omega$ , $\alpha$	$x=r\theta$ , $v=r\omega$ , $a=r\alpha$
$F=ma$	$\tau=I\alpha$	$W=Fd$ → $Work_{rot}=\tau\theta$
$K=\frac{1}{2}mv^2$	$K_{rot}=\frac{1}{2}I\omega^2$	$P=Fv$ → $P_{rot}=\tau\omega$

⚠️ Radians Only: All rotational equations require Radians (1 rev = $2\pi$ rad). Degrees = wrong answer.

2. Rotational Inertia ( $I$ )

Mass ( $m$ ) resists linear acceleration. Rotational Inertia ( $I$ ) resists angular acceleration. $I$ depends on mass and its distance from axis.

$I = \sum mr^2$

AP Physics 1 shapes: Disk $\frac{1}{2}MR^2$ , Hoop $MR^2$ , Sphere $\frac{2}{5}MR^2$

Diagram comparing moment of inertia: solid sphere (2/5 MR²) vs hollow hoop (MR²). Hoop harder to spin.

Mass Farther = Harder to Spin: Hoop ( $I=MR^2$ ) > Sphere ( $I=\frac{2}{5}MR^2$ ).

3. Newton’s 2nd Law for Rotation

$\tau_{net} = I\alpha$

Net torque causes angular acceleration, just like $F_{net}=ma$ .

4. Rotational Kinetic Energy & Rolling

$K_{total} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$

Rolling without slipping: $v=r\omega$ . Hoop slower than sphere down ramps.

Wheel rolling without slipping: bottom v=0, top v=2v_center.

Rolling Condition: $v=r\omega$ . Friction provides torque, no slipping.

5. Quick AP Practice

📚 AP Practice Problems

1. Sphere vs hoop (same $M$ , $R$ ) roll down ramp. Which wins?

Answer

Sphere ( $I=\frac{2}{5}MR^2$ < Hoop $MR^2$ ). Less energy to rotation = more to translation = faster.

2. 120 rpm wheel. Angular velocity (rad/s)?

Answer

$120 \frac{rev}{min} \times \frac{2\pi rad}{rev} \times \frac{1 min}{60 s} = 4\pi \approx 12.6 \, rad/s$

3. Disk $I=\frac{1}{2}MR^2$ , hoop $I=MR^2$ . Which harder to spin?

Answer

Hoop. Higher $I$ = more torque needed for same $\alpha$ ( $\tau=I\alpha$ ).

🔗 Related AP Physics Resources

Unit 7 Part 2 Complete!

You mastered rotational kinematics, inertia, and energy. Final piece: rotational momentum conservation.

Next: Angular Momentum →