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## Causing Rotational Motion

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**Causing Rotational Motion**• In order to make an object start rotating about an axis, a force is required • However, not only the amount of force applied but also the position from the axis to which it is applied is important in determining the amount of rotation (angular acceleration • Distance from axis is called the Lever Arm**Torque Definition**• Combination of amount of force and distance from axis is called Torque (τ) • A torque is necessary in order to provide angular acceleration • τ = rF r- dist from axis • Units - N m • In order to use this equation, the force must be perpendicular to the axis of rotation**Example 1**• A biceps muscle exerts a vertical force on the lower arm as shown. Calculate the torque acting on the lower arm if the muscle is attached 5.0 cm from the elbow.**Example 2**• A wrench is pulled by a force of 30 N at an angle of 30° with the axis and a distance of 15cm from its pivot end. What torque is acting on it?**Equilibrium**• Occurs when total force acting balance and no rotational motion occurs • In order for equilibrium to exist, the total torque acting in the clockwise direction must balance the total torque acting in the counterclockwise direction**See-Saw**• When stationary, the total τ clockwise is equal to the τ counterclockwise • If kid A pushes up with more force, the τ is no longer balanced (more force clockwise) and the see-saw begins to rotate clockwise with an angular velocity**Example 3**• Two people are sitting on a seesaw that is 2.5 m long. One has a mass of 40 kg and the other a mass of 60 kg. Where would the support on the see-saw need to be placed in order to produce equilibrium?**Example 4**• A 7.0 m beam is hanging from the ceiling by two ropes on its ends. The bar has a mass of 300 kg and it is non-uniform, with its center of mass 3.0 m from one end. A 400kg mass is hung from the beam’s light end and a 200 kg mass is hung from its heavy end. What force is acting on each rope?