Torque. 1. Torque - To make an object rotate, we must apply a force at a certain distance away from the axis => ex) opening a door

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1 Torque Level : Conceptual Physics Teacher : Kim 1. Torque - To make an object rotate, we must apply a force at a certain distance away from the axis => ex) opening a door Torque is defined as τ = r F where r is the distance between the axis to the point where the force if applied Torque is the measurement of the force to produce rotation around an object around an axis. Axis F This is the reason why the doorknob is position as far away from the axis (hinge of the door) as possible. Unit for torque is [N.m] r *~ To unscrew a bolt, we need to rotate the bolt. Whenever you want to rotate any object, you must apply a torque on the object. Q1) Calculate the torque produced by a 50N perpendicular force at the end of a 0.08m long wrench. Use τ = r F a) 4N m b) 12N m c) 25N m d) 35N m 0.08m Push with 50N of force! Q2) Calculate the torque produced by a 50N perpendicular force at the end of a 0.1m long wrench. Use τ = r F a) 10N m b) 5N m c) 2N m d) 0.5N m 0.1m Push with 50N of force! Q3) To unscrew a bolt, you need to apply a torque. Let s say a bolt needs 42N.m of torque to be unscrewed. i) If the length of the wrench you have is 0.15m and the maximum strength you can apply on the handle is 200N, will the bolt become loosened? If not, you need to get a longer wrench. How long must be the wrench in order to loosen the bolt?

2 τ = r F 2. Net Torque *~There can be more than one torque acting on an object Q4) A meter-stick is pivoted at the center. Any unbalance 10N of pushing force are applied as shown at the edge at both ends, find the net torque acting on the system. (and which direction? clockwise or counter-clockwise?) a) 10N m b) 15N m c) 20N m d) 25N m *~1m =100cm Q5) A meter-stick is pivoted at the center. Any unbalance torque applied will result in rotating the meterstick. If 15N and 10N of pushing force are applied as shown at the edge at both ends, find the net torque acting on the system. (and which direction? clockwise or counter-clockwise?) a) 1.0N m b) 1.5N m c) 2.0N m d) 2.5N m F=15N Q6) A meter-stick is pivoted at the center. Any unbalance 10N of pushing force are applied as shown, find the net torque acting on the system. (and which direction? clockwise or counter-clockwise?) a) 10N m b) 8N m c) 6N m d) 4N m 0.3m Q7) A meter-stick is pivoted at the center. Any unbalance 15N and 10N of pushing force are applied as shown, find the net torque acting on the system. (and which direction? clockwise or counter-clockwise?) a) 1.0N m b) 1.5N m c) 2.0N m d) 2.5N m F=15N 0.2m

3 3. Balance Net Torque i) If the stick does not move, the system is in equilibrium. This can only be possible if the net torque is zero. That is, the torque produce on the left of the axis and the right of axis must be equal but opposite direction. r1 axis r2 F2 F1 ii) If you balance a meter-stick on a fulcrum and hang objects on both sides, the weight of the object will produce net torque. (F g=mg) If you shift the position of the two objects, until the meter-stick balance, the net torque will be zero. By using this theory, we can measure the mass of the unknown objects by hanging known objects until they balance axis left = right => Example) A meter-stick is placed on a fulcrum at the 50cm mark. If the mass m is placed so that the whole system is in equilibrium, then the torque on the left and the torque on the right is equal. Find the unknown mass. 1meter=100cm, g=9.8m/s 2 10cm 50cm 80cm 2kg m=? Sol) A torque on the left of the axis exists due to the gravitational force F g pulling on the 2kg object over a distance of 0.4m. A torque on the right of the axis exists due to the gravitational force F g pulling on the block of unknown mass over a distance of 0.3m. If the block is placed so that the system is balanced, then left = right. Since torque is defined as τ = r F and the force F in this system is F g=mg, Solving for m gives m=2.67kg m leftg r left = m right g r right => = m

4 left = right => Q8) A meter-stick is placed on a fulcrum at the 50cm mark. If the mass m is placed so that the whole system is in equilibrium, then the torque on the left and the torque on the right is equal. Find the unknown mass. 1meter=100cm, g=9.8m/s 2 0cm 50cm 75cm m=1kg m=? a) 4kg b) 2kg c) 1kg d) 0.5kg Q9) A meter-stick is placed on a fulcrum at the 25cm mark. If the mass of 1kg is placed at the 0cm so that the whole system is in equilibrium, then the torque on the left and the torque on the right is equal. Find the mass of the meter-stick. 1meter=100cm, g=9.8m/s 2 COM of the meter-stick!! 25cm 50cm 100cm m=1kg a) 4kg b) 2kg c) 1kg d) 0.5kg

5 left = right => Q10) A meter-stick is placed on a fulcrum at the 20cm mark. Find the mass of the meter-stick COM of the meter-stick!! 10cm 20cm 50cm 0.5kg F g a) 0.85kg b) 0.36kg c) 0.17kg d) 0.08kg