Rotational Motion Chapter 8

Rotational Variables

Comparison between Linear and Rotational Variables Quantity Linear Variables Rotational Variables Relationship Displacement Velocity Acceleration

Example Problems  8-5. A movie lasts two hours. During that time, what is the angular displacement of each of the following:  a. the hour hand of a watch  b. the minute hand of a watch.  8-6. The Moon rotates once on its axis in 27.3 days. Its radius is 1.74 X 10 6 meters.  a. What is the period of the Moon’s rotation in seconds?  b. What is the frequency of the Moon’s rotation in rad/s?  c. What is the linear speed of a rock on the Moon’s equator due only to the Moon’s rotation?  d. Compare this to the speed of a person at the Earth’s equator due to the Earth’s rotation

Example Problems - 2  8-9. In the spin cycle of a clothes washer, the drum turns at 635 rev/min. If the lid of the washer is opened, the lid of the washer is opened, the washer turns off. If the drum requires 8.0 s to come to a stop, what is the angular acceleration of the drum?  A CD-ROM has a spiral track that starts 2.7 cm from the center of the disk and end 5.5 cm from the center. The disk drive must turn the disk so that the linear velocity of the track is a constant 1.4 m/s. Find the following:  a. the angular velocity of the disk for the start of the track.  b. the angular velocity of the disk for the end of the track.  c. the angular acceleration if the track plays for 76 min.

Torque

Balanced Torques  Torques are balanced if the sum of torques that tend to produce a clockwise rotation is equal to the sum of the torques that produces a counterclockwise rotation. If torques are balanced there is no rotation. 30 cm 20 N? N 40 cm

Today’s Activities  Center of Mass Builder Center of Mass Builder  Balancing Act simulation Balancing Act simulation  Torque Worksheet  Useful video: Solving Torque ProblemsSolving Torque Problems

Moment of Inertia

Examples of Rotational Inertia

Newton’s Second Law for Rotation

Example Problems  A disk with a moment of inertia of 0.26 kg-m 2 is attached to a smaller disk mounted on the same axle. The smaller disk has a diameter of m and a mass of 2.5 kg. A strap is wrapped around the smaller disk as shown in Figure Find the force needed to give this system an angular acceleration of 2.57 rad/s 2.  A rope is wrapped around a pulley and pulled with a force of 13.0 N. The pulley’s radius is m. The pulley’s rotational speed goes from 0.0 rev/min to 14.0 rev/min in 4.50 s. What is the moment of inertia of the pulley?

Center of Gravity/Center of Mass

Finding the Center of Mass

Center of Mass Applications  Fosbury Flop Fosbury Flop  Fosbury Flop Fosbury Flop  Science of NFL Football Science of NFL Football  Circus Physics Circus Physics  Pluto and Charon Pluto and Charon

Example Problem  A 7.3 kg ladder, 1.92 m long, rests on two sawhorses as shown. Sawhorse A is located 0.30 m from the end, and sawhorse B is located 0.45 m from the other end. Choose the axis of rotation to be the center of mass of the ladder. A. What are the torques acting on the ladder? B. Write the equation for rotational equilibrium. C. Solve the equation for F A in terms of F g. D. How would the forces exerted by the two sawhorses change if A were moved very close to, but not under the center of mass? 0.30 m0.66 m0.51 m0.45 m AB CoM

Stability and Equilibrium  An object balanced so that any displacement lowers its center of gravity is in unstable equilibrium.  An object balanced so that any displacement raises its center of gravity is in stable equilibrium.  An object that is balanced so that any displacement neither raises or lowers its center of gravity is in neutral equilibrium.  An object with a low center of gravity is usually more stable than an object with a nigh center of gravity.  If the center of gravity extends beyond the support base of an object, the object will topple.