PHY131H1S – Class 18 Rotational Motion

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PHY131H1S – Class 18 Little intro Ch.12 vocabulary quiz… Today: • Rotational Motion, Moment of inertia is Rotational Energy • Centre of Mass A. the rotational equivalent of mass. B. the point at which all forces appear to act. • Moment of Inertia C. the time at which inertia occurs. D. an alternative term for moment arm. Problem Set 7 on MasteringPhysics due Friday at 11:59PM Rotational Motion An object rotates about an axis. The change in angle is the same for any point on the object. Its angular velocity is The units of ω are rad/s. If the rotation of the object is speeding up or slowing down, its angular acceleration is The units of α are rad/s2. Center of Mass The center of mass is the mass-weighted center of the object. 1 Rotation About the Center of Mass Rotational Energy A rotating rigid body has kinetic energy because all atoms An unconstrained object in the object are in motion. The kinetic energy due to (i.e., one not on an axle or a rotation is called rotational kinetic energy. pivot) on which there is no net force rotates about a point called the center of mass. The center of mass remains motionless while Here the quantity I is called the object’s moment of inertia. every other point in the object undergoes circular motion around it. The units of moment of inertia are kg m2. An object’s moment of inertia depends on the axis of rotation. Example Important Concepts A ninja-star with mass = 250 g, moment of inertia 8.5 x 10-4 kg m2, begins at rest, and then is thrown. The throw takes 0.20 s, and after the throw the star has v = 25 m/s, and spins 15 times per second. a) What was the angular acceleration during the throw? b) What is the final total kinetic energy of the star? Note: Total kinetic is Klinear + Krotational 2 Four Ts are made from two identical rods of equal mass and length. Rank in order, from Updated Conservation of Energy… largest to smallest, the moments of inertia Ia to Id for rotation about the dotted line. 1/3 mL2 1/3 mL2 0 M(L/2)2 + mL2 + 0 + 1/12 mL2 + 1/3 mL2 (a)= 4/3 mL2 (b) = 1/3 mL2 (c)= 1/12 mL2 (d) = 7/12 mL2 A. Ia > Id > Ib > Ic B. Ic = Id > Ia = Ib C. Ia = Ib > Ic = Id D. Ia > Ib > Id > Ic E. Ic > Ib > Id > Ia Ultimate Soup Can race: Cream of Mush vs. Chicken Broth!! • Two soup cans begin at the top of an incline, are released from rest, and allowed to roll without slipping down to the bottom. Which will win? • Both cans have about the same mass and moment of inertia. • Cream of Mushroom soup is more of a thick paste, so when this can is rolling down the ramp, the soup rotates along with the can as one solid object, like a solid cylinder. • The Chicken Broth is more of a liquid, so the metal can rolls, while the liquid stays oriented up and down without rotating. Predict: A. Cream of Mushroom will win B. Chicken Broth will win C. Both will reach the bottom at about the same time. 3.

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