Question

The drawing shows two identical systems of objects; each consistsof the same three small balls connected by massless rods. In bothsystems the axis is perpendicular to the page, but it is located ata different place, as shown. The same force ofmagnitude F is applied to the same ball in eachsystem (see the drawing). The masses of the ballsare m₁ = 8.4 kg, m₂ = 5.2 kg,and m₃ = 5.0 kg. The magnitude of the forceis F = 446 N. (a) For each of the two systems,determine the moment of inertia about the given axis of rotation.(b) Calculate the torque (magnitude and direction) acting on eachsystem. (c) Both systems start from rest, and the direction of theforce moves with the system and always points along the 4.00-m rod.What is the angular velocity of each system after 5.19 s?

(a)	IA	=	---Select---N · m^2kg · m^2N · mkg
	IB	=	---Select---kg · m^2N · m^2N · mkg
(b)	τA	=	---Select---N · m^2kg · m^2kgN · m
	τB	=	---Select---N · mN · m^2kgkg · m^2
(c)	ωA	=	---Select---rad/s^2m/srad/srad
	ωB	=	---Select---rad/srad/s^2m/srad

Answer 1

(a)
   the moment of inertia of each system will be
   for the system A
   I = m₁ r₁²+ m₂r₂² + m₃r₃²
     = (8.40 kg) (0 m)² + (5.2kg) (3.00 m)² + (5.00 kg) (5.00 m)²
     = ......... kg.m²
   for the system B
   I = m₁ r₁²+ m₂r₂² + m₃r₃²
     = (8.4 kg) (5.00 m)² +(5.2 kg) (4.00 m)² + (5.0 kg) (0 m)²
     = ......... kg.m²
(b)
   if same force of magnitude F = 446 N the torque willnot be the saeme
   we know that
   τ = F l
   where l = 3.00 m
   in the system B the lever arm is l = 0,since the line of action of the force passes through the axis
   of rotation
   for the system A the torque will be
   τ = - F l
      = - (446 N) (3.00 m)
      = ....... N.m
   for the system B the torque will be
   τ = F l
      = (446 N) (0 m)
      = 0 N.m

(c)
   the equation for the angular velocity is givennby

   ω = ω_o + α t
   but α = (Σ τ / I)

   where Σ τ is the net torque and I is themoment of inertia
   in both the systems start from rest the initialangular velocity ω_o = 0 rad/s

   final angular velocity are after t = 10 s
   for system A

    ω = ω_o + (Στ / I) t
        = ........ rad/s

   for system B
    ω = ω_o + (Στ / I) t
        = ........ rad/s