Torque is the rotational equivalent of force, causing objects to spin around an axis. It's calculated using the force applied and its distance from the rotation point. Understanding torque is crucial for analyzing everything from door hinges to planetary orbits.

Net torque determines an object's angular acceleration, just like net force affects linear acceleration. By summing individual torques and considering an object's resistance to rotation, we can predict how quickly it will spin up or slow down.

Understanding Torque and Angular Acceleration

Definition and effects of torque

• Torque causes angular acceleration and rotates objects around an axis
• Calculated using $τ = r × F$ or $τ = rF sin θ$ where r is distance from axis to force line, F is applied force, θ is angle between force vector and lever arm
• Larger torque produces greater angular acceleration
• Direction of torque determines rotation direction (clockwise or counterclockwise)

Calculation of net torque

• Net torque sums all individual torques acting on an object $τ_net = Σ τ_i$
• Clockwise torques negative, counterclockwise positive
• Steps to calculate:

1. Identify all forces
2. Determine lever arm for each
3. Calculate individual torques
4. Sum torques, considering sign

• Examples: door handle, wrench turning bolt

Angular acceleration from Newton's law

• Rotational form: $τ_net = Iα$ where I is moment of inertia, α is angular acceleration
• Moment of inertia measures resistance to rotational acceleration based on mass distribution
• Angular acceleration calculated as $α = τ_net / I$
• Factors: magnitude of net torque, object's moment of inertia
• Examples: spinning ice skater, merry-go-round

Problems with rotational dynamics

• Approach: identify given info, choose equations, solve for unknowns
• Key equations: $τ = rF sin θ$, $τ_net = Iα$, $α = τ_net / I$
• Common problems: finding net torque, calculating angular acceleration, determining force for specific acceleration
• Consider multiple forces, changing moment of inertia, rotational equilibrium ($τ_net = 0$)
• Examples: balancing seesaw, accelerating flywheel, stopping rotating platform