Learning Objective:
Analyse forces in horizontal circular motion using a conical pendulum and banked curves.
Conical Pendulum
Banked Curve
Conical Pendulum
String Length L:
1.0 m
Mass m:
0.5 kg
Angular Velocity ω:
3.0 rad/s
Angle θ
0°
Tension T
0 N
Centripetal Force Fc
0 N
Radius r
0 m
tan(θ) = ω²r/g
T = mg/cos(θ)
Fc = mω²r
Animation & Free-Body Diagram
r
θ
T
mg
Fc
→ Red
= Tension T
→ Blue
= Weight mg
→ Green
= Fc = T sin(θ)
Banked Curve
Bank Angle β:
15°
Speed v:
15 m/s
Radius r:
50 m
Ideal Speed (no friction)
0 m/s
Required Friction
0 N
Normal Force N
0 N
Centripetal Force
0 N
v
ideal
= √(gr·tan β)
N = mg/cos(β)
At ideal speed, no friction is needed!
Banked Curve Diagram
N
mg
f
β
→ N
= Normal force
→ mg
= Weight
→ f
= Friction