Torque type shi

What is torque?

Torque is the tendency of a force to cause rotation around a pivot point.

What is the equation for torque?

τ=rFsinθ

What is the lever arm?

The perpendicular distance from the pivot to the line of action of the force.

d=rsin⁡θd = r\sin\thetad=rsinθ

Alternate torque equation using lever arm

τ=Fd

What are the two conditions for mechanical equilibrium?

1. Net force equals zero Σ F= 0

2. Net torque equals zero ΣT=0

What equations come from the equilibrium conditions?

1. Σ Fx = 0

2. Σ Fy =0

3. Σ T = 0

What is moment of inertia?

Moment of inertia is rotational mass—- resistance to rotational acceleration I = Σ mr²

Relationship between torque and angular acceleration

Σ T= Ia Rotational version of Newton's 2nd Law.

What is rotational kinetic energy?

KEr = ½ Iw² I = moment of inertia w= angular velocity

What energies exist in a rotating system

1. Translational kinetic energy KEt

2. Rotational kinetic energy KEr

3. Potentional energy PE

Conservation of mechanical energy for rotational systems

(KEt​+KEr​+PE)i​=(KEt​+KEr​+PE)f​

Work-energy theorem with nonconservative forces

Wnc = ΔKEt​+ΔKEr​+ΔPE

What is angular momentum?

L=Iω

What happens if net external torque = 0?

Angular momentum is conserved.

Li=Lf

Equation used in angular momentum conservation problems

Ii​ωi​=If​ωf​

Relationship between torque and angular momentum

τ=ΔL​/Δt