Torque and rotational inertia 

Intros
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Lessons
  1. Definition of "Torque"
  2. Rotational Inertia
Examples
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Lessons
  1. A person exerts a force of 45N on the handle of a door 65cm wide.
    1. What is the magnitude of the torque if the force is exerted perpendicular to the door?
    2. What is the magnitude of the torque if the force is exerted at a 35°?
  2. Calculate the net torque about the axle of the of the wheel shown below. Assume that a friction torque of 0.60 N.mN.m opposes the motion.

    Torque and Rotational Inertia
  3. A torque of 66 N.mN.m is required to tighten the bolts on the cylinder head of a car engine. The wrench used to tighten the bolt is 26cm long.

    Torque and Rotational Inertia
    1. What is the perpendicular force that is exerted by the mechanics to the end of the wrench to tighten the bolts?
    2. If the six-sided bolt head has a diameter of 20mm, how much force will be applied near each of the six points?
  4. Two small weights of mass 4.0kg and 6.0kg are mounted 6.0m apart on a light rod as shown below. Calculate the moment of inertia of the system;

    Torque and Rotational Inertia
    1. When rotated about an axis halfway between the weights.
    2. When rotated about an axis 0.40m to the left of the 4.0kg mass.
  5. A 12.0N force is applied to a cord wrapped around a pulley of mass MM = 6.00kg and radius RR= 22.0cm. The pulley accelerates uniformly from rest to an angular speed of 40.0 rad/s in 2.00s. If there is a frictional torques τfr\tau _{fr} = 1.20m.Nm.N at the axle, determine the moment of inertia of the pulley as it rotates around its center.
  6. Determine the moment of inertia for the following uniform objects:
    1. A 12.80 kg sphere of radius 0.464m rotating through its center.
    2. A bicycle wheel 88.2cm in diameter. The rim and tire have a combined mass of 1.36kg
    3. A helicopter rotor blade (long thin rod), 2.76 m long and has a mass of 140kg.
  7. An Atwood's machine consists of two masses, m1m_{1} = 4.0kg and m2m_{2} = 7.0kg, which are connected by a massless inelastic cord that passes over a pulley. The pulley has radius RR = 0.4m and moment of inertia II =4.0 kg. m2m_{2} about its axle.

    Torque and Rotational Inertia
    1. Determine the acceleration of the masses m1m_{1} and m2m_{2}.
    2. Find tensions supporting m1m_{1} and m2m_{2}.