Section 5.6: Problem-Solving Strategies
This section presents systematic approaches for solving rotational dynamics and angular momentum problems efficiently.
- Identify the type of motion (rotational, angular momentum, torque).
- List known quantities: I, ω, τ, α, L, etc.
- Determine which conservation laws or equations apply.
- Draw diagrams showing forces and torques.
- Apply step-by-step calculations, checking units.
- Verify answers for physical consistency.
Example 1
Disk of I = 4 kg·m², ω = 3 rad/s. Torque τ = 6 N·m is applied for 2 s. Find final ω.
Angular acceleration: \( \alpha = \tau / I = 6 / 4 = 1.5 \, \text{rad/s²} \)
Final ω: \( \omega_f = \omega_i + \alpha t = 3 + 1.5*2 = 6 \, \text{rad/s} \)
Example 2
Figure skater spins at ω = 2 rad/s, I = 5 kg·m². Pulls arms in, I = 2 kg·m². Find new ω.
Use conservation of angular momentum: \( I_i \omega_i = I_f \omega_f \)
\( \omega_f = 5*2/2 = 5 \, \text{rad/s} \)
Practice Problems
- Wheel, I = 3 kg·m², ω = 4 rad/s. Torque 2 N·m for 3 s. Find ω_f.
- Disk, I = 6 kg·m², ω = 2 rad/s. Another disk I = 2 kg·m² placed on top. Find ω_f.
- Rod, I = 5 kg·m², torque 10 N·m, time 1.5 s. Compute final angular speed.
- Skater, I = 4 kg·m², ω = 3 rad/s. Arms in, I = 1.5 kg·m². Find ω_f.
- Flywheel, I = 8 kg·m², τ = 4 N·m, t = 5 s. Determine ω_f from rest.