Question

Do 3.

PHYS 141-Physies Kaul Lecture Supplement/Worksheet 6Intre Cireular Motion A 1. Define and provide an example of each of the qeantisies belorw and discess their differences. Alvo, draw a vector diagram for each example showing any change in velocity vectors, and showing the centripetal acceleration vector wr to your velocity vectors if i. son mo. b) c) 2. Circular Motion Quantities. Define each of the following quantities used in circular motion and state the base units used in each case. Are these vector quantities? If so, how is direction determined in each case? a) Angular displacement (average vs instantaneous) b) Angular velocity) e) Angular acceleration ") 3. Cireular Motion on a Clock. Consider a traditional wall clock face with a second and minute hand. Do the following: a) Find the angular displacement of each hand for from I b) Find the angular velocity and speed of each hand from 12 o'clock position to the 3 o'elock position c) Find the angular acceleration of each hand from 12 o'clock position to the 3 o' clock position between circular motion quantities and translational (linear) motion quantities? What relations exist between angular and translational velocity? What relations exist between angular and translational acceleration? How does angular acceleration differ from centripetal acceleration? What is a rigid body and why is it important in circular motion? 5. Circular Motion and Wheel Comparisons. An auto is travelling west at 60 km/hr a) What is the angular velocity of the 0.3m radius wheels? b) If the wheels had a 0.5 m radius, what then would the angular velocity be? c) If the 0.3 m radius wheel auto accelerates uniformly from 60 km/hr to 70 km/hr in 4.0 s, what is its angular acceleration? 6. Circular Kinematics. A CD spins at a constant speed of 60 rad/s. Do the following: a) Find how fast the CD spins in rpm. b) Find how long it takes for the CD to complete 1 revolution and its frequency of oscillation? c) Find the linear speed of the CD at the position of 3.0 cm from the center. If the angular speed changes, what impact does that have on the linear speed (as it does in compact dise players when the read head moves from the center of the disc)? d) Find the linear speed of the CD at a position of 5.0 cm from the center. How does this differ from your answer in c)? e) What is the angular acceleration of the CD if it changes its angular speed from 60 rad's to 80 rad/s in 2 min (assuming angular acceleration is uniform)? D What is the centripetal acceleration an ant on the CD at the position of 3.0 em from the center would experience?

Answer 1

a) the hour hand turned through 90 degrees. The minute hand completed 3*60 = 180 rounds. In one round the angular displacement is 360 degrees so the angular displacement is 360*180 = 64800 degrees. The second hand completed 3*3600 = 10800 rounds. The angular displacement is 360*10800 = 3888000 degrees

b) Time taken by all of the hand is 3 hrs. so the velocity of the hour hand is 90 / 3 = 60 degrees/hour$=0.33\pi \ rad/hr$

for minute hand 64800/3 = 21600 degrees / hour$=120\pi \ rad/hr$

for second hand 3888000/3 = 1296000 degrees/hour$=7200\pi \ rad/hr$

c) Since all of the hands are moving with a constant velocity so the angular acceleration should be zero for all hands.