Lab VI

PHYSICS 001 LAB REPORT NAME: Brandan Seemungal ID: @03071168 LAB: Rotation and Torque

Objective: To analyze the balance of a meter stick and calculate the mass of an object subject to the meter stick’s center of gravity. Theory: When a rigid body with a fixed pivot point O, is acted upon by a force, there may be a rotational change in velocity of the rigid body. In the diagram below, there is a force 𝐹⃗ that is applied to the arm of the lever. The position relative to the pivot point O is defined by a vector 𝑟⃗ . The two make an angle with each other 𝜑 ( 𝐹⃗ is in the plane of the paper). 𝐹⃗ may be resolved into two components. The radial component 𝐹𝑟 points along 𝑟⃗ and does not rotate. The tangential component 𝐹𝑡 is perpendicular to 𝑟⃗ and has the magnitude 𝐹𝑡 = 𝐹 ∗ sin 𝜑 . This component does cause rotation. The quantity 𝜏 is defined as 𝜏 = ( 𝑟 )( 𝐹 ∗ sin 𝜑 ) There are two other ways of computing torque, 𝜏 = ( 𝑟 )( 𝐹 ∗ sin 𝜑 ) = 𝑟 ∗ 𝐹𝑡 𝜏 = ( 𝑟 ∗ sin 𝜑 )( 𝐹 ) = 𝑟⊥ ∗ 𝐹 Where we have 𝑟⊥ as a perpendicular distance between the rotation axis at the pivot and a line extended from 𝐹⃗ . The extended line is the line of action of 𝐹⃗ and 𝑟⊥ is the moment arm of 𝐹⃗ .Torque means “to twist” and has the unit of N ∗ m. Do not confuse the units of torque with the units of energy as Joule, J is defined as 𝑁 ∗ 𝑚 . Torque is defined as positive if rotating counter-clockwise and negative if clockwise. Torque obeys the superposition principle, therefore when several torques act on a body, the net torque or resultant torque is the sum of the individual torques.

Positions Distance to Fulcrum 46.8g Fulcrum 50g COG 50g Mass of meter stick 40 21.4 9.54 18.6 97.48 37 12.1 12.54 24.9 34 3.4 15.54 30.6 44 32.7 5.54 11.3 47 41.5 2.54 5.5 Part III 1. Hang a 75 g mass from one hanger and an unknown mass from the second hanger. Balance the meter stick at a position other than the center of gravity and make sure that the fulcrum is always to the left of the COG, otherwise the equation does not hold. Determine the distances from the weight hangers to the fulcrum. Determine the unknown weight using the conditions of equilibrium. Positions Distance to Fulcrum 66.2g Fulcrum 75g Unknown COG 75G Unknown 45 30 55.2 4.54 15 10.2 45 20 76.3 4.54 25 31.3 40 18.7 50 9.54 21.3 10 46 25 64 3.54 21 18 40 14.4 55 9.54 25.6 15

Questions: 1. Why was the supporting force exerted on the meter stick by the sharp edge not considered in your calculations? The supporting force exerted on the meter stick by the sharp edge was not taken into account due to the fact that the torque exerted by the sharp edge would be zero, as it’s aligned with the axis point of the meter stick. 2. A meter stick is pivoted at its 50 cm mark but does not balance because of non-uniformities in its material that cause its center of gravity to be displaced from its geometrical center. However, when weights of 150 g and 300 g are placed at the 10 cm and 75 cm marks, respectively, balance is obtained. The weights are then interchanged and balance is again obtained by shifting the pivot point to the 43 cm mark. Find the mass of the meter stick and the location of its center of gravity. Center of gravity = 48.4 cm Mass of meter stick = 940g