# ex 10 - PURPOSE OBJECTIVES A mass rotating in a circle is...

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PURPOSE/ OBJECTIVES A mass rotating in a circle is pulled into a smaller radius and the new angular speed id predicted using conservation of angular momentum. APPARATUS/EQUIPMENT - Smart Pulley Timer Program - Rotational Inertia Accessory (ME-8953) - Rotating Platform (ME-8951) - Smart Pulley - balance THEORY Angular momentum is conserved when the radius of the circle is changed. L = I i ω i = I f ω f Where I i is the initial rotational inertia and ω i is the initial angular speed. So the final rotational speed is given by: ω f = Ii If ωi To find the rotational inertia experimentally, a known torque is applied to the object and the resulting angular acceleration is measured. Since τ = Iα I= τ α Where α is the angular acceleration which is equal to a/r and τ is the torque caused by the weight hanging from the thread which is wrapped around the base of the apparatus. Τ = rT Where r is the radius of the cylinder about which the thread is wound and T is the tension in the thread when the apparatus is rotating.