Rotational Motion

Chapter 8

Describing Rotational Motion

8.1

Describing Rotational Motion

• Radian• Angular Displacement– change in an angle

Practice Problem

• What is the angular displacement in radians of a wagon that moves 135 around a circular path?

Angular Velocity

Practice Problem

• A playground merry-go-round makes two complete rotations in 9.6s. What is its angular velocity?

Angular Acceleration

Practice Problem

• A car increases in speed from rad/s to rad/s in 5.0 s. What is the angular acceleration of the car?

Homework

• Page 200– 5-9

Rotational Dynamics

8.2

Starting Rotation of Object

• lever arm– perpendicular distance from the axis of rotation to

the point where the force is exerted– L= rsinθ– θ=angle at which the force is applied!!!– r=distance to point where force is applied to axis

Torque

• measure of how effectively a force causes rotation– N*m– τ (tau)

Practice Problem

• How much torque is applied if a wrench applies a force of 240N at an angle of 60.0° from the perpendicular? The wrench is 32cm long.

Net Torque

• Net=Sum• decide on a positive & a negative rotation

direction• ∑τ=τ1+τ2

Practice Problem

• Ashok, whose mass is 43kg, sits 1.8m from the center of a seesaw. Steve, whose moss is 52 kg, wants to balance Ashok. How far from the center of the seesaw should Steve sit?

Homework

• Page 203: 12-15• Page 205: 17-20

The Moment of Inertia

• resistance to rotation• I• kg*m2

• different for different shapes• Point Mass– I=mr2

Practice Problem

• What is the moment of inertia of a hockey puck that has a mass of 170g, a thickness of 2.5 cm, and a diameter of 7.6 cm? The formula for the moment of inertia of a cylinder is I=1/2mr2.

Homework

• Page 208: problems 21-24

Newton’s Second Law of Rotation

• Replace Newton’s Second Law (F=ma) with angular terms

• a=α• F=τnet

• m=I

Practice Problem• A solid steel wheel has a mass of 15kg and a

diameter of 0.44m. It starts at rest. You want to make it rotate at 8.0 rev/s in 15s.– What torque must be applied to the wheel?– If you apply the torque by wrapping a strap

around the outside of the wheel, how much force should you exert on the strap?

– If the force on the strap were twice as great, what would be the speed of rotation of the wheel after 15s?

Equilibrium

8.3

Center of Mass

• the point on the object that moves in the same way that a point particle would move

• Locating– Suspend the object from a point, center of mass is

along the vertical line drawn– intersection of 2 vertical lines will give a point

• Center of mass for a person– different male & female

Center of Mass and Stability

• Stable– an external force is required to tip object

• Higher center of gravity– less force needed to upset

• Equilibrium– translational equilibrium– rotational equilibrium

Practice Problem

• A 5.8kg ladder, 1.80m long, rests on two sawhorses. Sawhorse A is 0.60m from one end of the ladder, and sawhorse B is 0.15m from the other end of the ladder. What force does each sawhorse exert?– What if the mass of the ladder is 11.4kg?

Homework

• Page 210: 26-29• Page 215: 37-39

Rotating Frame of Reference

• Centrifugal Force– apparent force (not real)– pulls toward the outside of the rotation

• Coriolis Effect– deflection of a moving object

Homework

• Page 217: 40-45• Page 223: 75, 78, 81, 84, 88

• MAKE SURE YOU STUDY FOR YOUR TEST TOMORROW!!!

• ***IF YOU HAVE QUESTIONS ASK***