Bellringer: What would be the net acceleration of a 15 g toy car down a 30 degree incline if the acceleration due to friction is 1.8 m/s 2 ? Include a.

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Presentation transcript:

Bellringer: What would be the net acceleration of a 15 g toy car down a 30 degree incline if the acceleration due to friction is 1.8 m/s 2 ? Include a free-body diagram of all forces.

Chapter 8 – Angular motion, torque, and moment of inertia

Angular Motion  What is angular motion? How is it different from linear motion?

Vocabulary  Revolution  Radian  Angular displacement  Angular velocity  Angular acceleration

Equations  1 revolution = 2π radians  Angular displacement (Θ, in rad) Θ = d/r (linear distance in m / radius)  Angular velocity (ω, in rad/s) ω = Θ/t (also equal to v/r)  Angular acceleration (α, in rad/s 2 ) α = ω/t (also equal to a/r)

Practice p.200 (1-3)  Keep answers to number 1 in terms of π

Bellringer  What is the equation to convert from linear distance to angular displacement?  What is the equation to convert from linear velocity to angular velocity?  What is the equation to convert from linear acceleration to angular acceleration? WHAT IS SIMILAR IN ALL OF THESE EQUATIONS?  Write out the equations to find angular velocity and to find angular acceleration. WHAT DO YOU NOTICE ABOUT THESE EQUATIONS?

Torque  What is torque? Definition Equation Lever arm (perpendicular distance from the axis of rotation to the point where the force is exerted) ○ L = r sin Θ when the angle is not perpendicular

Practice p.203 (11-15) 11. τ = 35 Nm, L = 25 cm, F = ? m o Nm 15.

Net Torque  To find net torque, use the equation: τ = Fg r  Use net torque when you have a situation with a center fulcrum and 2 lever arms

Practice p.205 (16-20) 16.m A = 43 kg, r A = 1.8 m, m S = 52 kg, r S = ? Nm kg kg N

Moment of Inertia  Definition  Equation  Compare and contrast the different moments of inertia for various objects in Table 8-2. What object would have the highest? Lowest? What does this mean about this object?

Practice p.208 (21 and 24) Units for moment of inertia are kgm What is the change in I when r is increased from 0.3 m to 0.6 m? 24.

Newton’s Second Law for Rotational Motion  What is Newton’s Second Law?  How does it change with rotational motion?

Practice p.210 (27)