Phys 101 Alanna Houston
October 25, 2007
- Moment of Inertia
- It is possible for a small force to exert a greater torque on a
system than a larger force.
- Consider a two-mass problem where we have masses m1 and 3m1
connected by a rigid but massless rod of length r:
o What are the moments of inertia about the small mass?
o What are the moments of inertia about the larger mass?
o What are the moments of inertia about the midpoint of the
- Moment of inertia depends on where the mass is located
- Some classics:
- Example: A cylindrical satellite (m = 3600 kg, r = 4.0 m) is ‘spun
up’ with four rocket motors firing tangentially. What is the force of
each rocket if the satellite is spun up from zero to 32 rpm in 5.0
minutes? Phys 101 Alanna Houston
o I = ½ mr^2 = ½ (3600)(4^2) = 28800 kg*m^2
o ω= ωo + αt, (32*2π)/60 = 5.0*60*α, α = 0.011 rad/s^2
o τ = Iα = 28800*0.011 = 317
o τ = 4F*r, F = τ/4r = 19.8N
- Wheelbarrows, Screwdrivers, and Bicycle Pedals all give
mechanical advantage that can be understood using the ideas of
- Why are sit-ups with your hands behind your head more difficult
than arms stretched in front of you?
o Putting mass at larger distance form pivot point (increased
moment of inertia) and therefore harder to turn at hips. With
larger moment of inertia, more difficult to spin and therefore
- Softball player swings bat, from rest to 3.0 rev/s in 0.20 seconds.
Bat is rod with m = 2.2 kg, of length 0.95 m. What is torque?
o ωo = 0 rad/s
o τ = Iα, α = Δω/Δt, α = 3*2π/0.20 = 94.2 rad/s^2
o I = 1/3 etc. FINISH
- Rotational kinetic energy is given by: