![]() First consider the free body diagram of the object and use SFNET = Macm : In the x direction Mg sin q - f = Macm Now consider rotation about the CM and use St = Ia realizing that t = Rf and a = aR R M q f IaRfR=2IafR=Mg qPhysics 101: Lecture 15, Pg 15 Rolling. It is an unknown, so we must solve for it. What is its acceleration? Consider CM motion and rotation about the CM separately when solving this problem q R I MPhysics 101: Lecture 15, Pg 14 Rolling. What is the velocity of the top of the wheel relative to the ground? A) -4 m/s B) -2 m/s C) 0 m/s D) +2m/s E) +4 m/s What is the velocity of the bottom of the wheel relative to the ground? A) -4 m/s B) -2 m/s C) 0 m/s D) +2m/s E) +4 m/s + 2 m/s -2 m/s 2 m/s 2 m/sPhysics 101: Lecture 15, Pg 13 Rolling An object with mass M, radius R, and moment of inertia I rolls without slipping down a plane inclined at an angle q with respect to horizontal. What is the velocity of the top of the wheel relative to the ground? What is the velocity of the bottom of the wheel relative to the ground? x y You now carry the spinning wheel to the right at 2 m/s. ![]() A) T1 T2 Compare the tensions T1 and T2 as block 3 falls A) T1 T2Physics 101: Lecture 15, Pg 12 Rolling A wheel is spinning clockwise such that the speed of the outer rim is 2 m/s. Compare the tensions T1 and T2 as the blocks are accelerated to the right by the force F. It takes force (torque) to accelerate the pulley. Using 1-D kinematics we can solve for the time required for the weight to fall a distance L: I m R T mg a a L L at=122tLa=2amRmRg=22Iwhere 20012y y v t at= Physics 101: Lecture 15, Pg 10 Torque ACT Which pulley will make it drop fastest? 1) Small pulley 2) Large pulley 3) Same 25 amRmRg=22ILarger R, gives larger acceleration.Physics 101: Lecture 15, Pg 11 Tension… m2 m1 T1 T2 T1 T1 since RT2 – RT1 = I2 a. ![]() For the hanging mass use SF = ma mg - T = ma For the flywheel use St = Ia TR sin(90) = Ia Realize that a = aR Now solve for a, eliminate T: I m R T mg a a L amRmRg=22ITRaR= IPhysics 101: Lecture 15, Pg 9 Falling weight & pulley. I m R T mg a a L What method should we use to solve this problem? A) Conservation of Energy (including rotational) B) tNet = Ia and then use kinematics Either would work, but since it asks for time, we will use B.Physics 101: Lecture 15, Pg 8 Falling weight & pulley. ![]() Starting at rest, how long does it take for the mass to fall a distance L. The moment of inertia of the pulley + flywheel is I. What is angular acceleration?Physics 101: Lecture 15, Pg 7 Falling weight & pulley A mass m is hung by a string that is wrapped around a pulley of radius R attached to a heavy flywheel. 29% 63% 8% Key idea: higher angular acceleration means more difficult to balance. Angular acceleration is smaller Why am I balancing a hammer on my finger? It sounds dangerous.Physics 101: Lecture 15, Pg 6 The Hammer! You want to balance a hammer on the tip of your finger, which way is easier A) Head up B) Head down C) Same t = I a m g R sin(q) = mR2 a mg R Torque increases with R Inertia increases as R2 g sin(q) / R = a Angular acceleration decreases with R! So large R is easier to balance. I just tried it in my home and I guess it is easier to balance the hammer with the head up. Problems Solved Like Newton’s 2nd Draw FBD Write Newton’s 2nd LawPhysics 101: Lecture 15, Pg 5 The Hammer! You want to balance a hammer on the tip of your finger, which way is easier A) Head up B) Head down C) Same 29% 63% 8% the larger the radius the larger the moment of inertia. Large I means hard to start or stop from spinning. Physics 101: Lecture 15, Pg 1 Physics 101: Lecture 15 Rolling Objects Today’s lecture will cover Textbook Chapter 8.5-8.7 Exam IIPhysics 101: Lecture 15, Pg 2 Overview Review Krotation = ½ I w2 Torque = Force that causes rotation t = F r sin q Equilibrium FNet = 0 tNet = 0 Today tNet = I a (rotational F = ma) Energy conservation revisitedPhysics 101: Lecture 15, Pg 3 Linear and Angular Linear Angular Displacement x q Velocity v w Acceleration a a Inertia m I KE ½ m v2 ½ I w2 N2L F=ma t = Ia Momentum p = mv L = Iw TodayPhysics 101: Lecture 15, Pg 4 Rotational Form Newton’s 2nd Law tNet = I a Torque is amount of twist provide by a force » Signs: positive = CCW Moment of Inertia like mass.
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