1. PHYSICS 231 Lecture 15: Rotations
Remco Zegers Walk-in hour Tue 4-5 pm helproom
PHY 231

2. Impulse (the change in momentum) p= Ft
Chapter 6 in one slide
Momentum p=mv
F=p/t
Impulse (the change in momentum) p= Ft
Types of collisions
Inelastic collisions
Elastic collisions
Momentum is conserved
Some energy is lost in the collision: KE not conserved
Perfectly inelastic: the objects stick
together.
Momentum is conserved
No energy is lost in the collision: KE conserved
Conservation of momentum: m1v1i+m2v2i=m1v1f+m2v2f
Conservation of KE: ½m1v1i2+½m2v2i2=½m1v1f2+½m2v2f2
Conservation of momentum: m1v1i+m2v2i=(m1+m2)vf
(v1i-v2i)=(v2f-v1f)
PHY 231

3. =s/r Radians & Radius Circumference=2r Part s=r r s   in radians!
360o=2 rad = 6.28… rad
 (rad) = /180o  (deg)
PHY 231

4. Angular speed and acceleration
Average angular
velocity
Instantaneous
Angular velocity
Angular velocity : rad/s
rev/s
rpm (revolutions per
minute)
PHY 231

5. example What is the angular velocity of earth around the sun?
Give in rad/s, rev/s and rpm
Answer: in 1 year, the earth makes one full orbit around the
sun.
= 2 rad/1 year rev/1 year 1 rev/1 year
= 2 rad/(3.2E+7 s) 1 rev/(3.2E+7 s) 1 rev/(5.3E+5 min)
= 2.0E-07 rad/s E-8 rev/s E-6 rpm
rad/s
rev/s
rpm
PHY 231

6. Angular acceleration
Definition: The change in angular velocity per time unit
Average angular
acceleration
Instantaneous angular
acceleration
Unit: rad/s2
PHY 231

7. Equations of motion Linear motion Angular motion (t)= (0)+(0)t+½t2
X(t)=x(0)+v(0)t+½at2
V(t)=V(0)+at
PHY 231

8. example A person is rotating a wheel. The
handle is initially at =90o. For 5s
the wheel gets an constant angular
acceleration of 1 rad/s2. After that
The angular velocity is constant.
Through what angle will the wheel
have rotated after 10s.
=0 
PHY 231

9. question An object is rotating over a circle with radius of 2 m.
Its speed is 1.5 rad/s. After 4 seconds, how many
rotations did the object make? 2 3 4 8 12
PHY 231

10. Angular Linear velocities
V is called the tangential velocity
PHY 231

11. Angular linear acceleration
velocity
Change in velocity
Change in velocity per time unit
acceleration
The linear acceleration equals the angular acceleration
times the radius of the orbit
PHY 231

12. example a b 5m 6m The angular velocity of a is 2 rad/s.
a) What is its tangential velocity?
If b is keeping pace with a,
b) What is its angular velocity?
c) What is its linear velocity? 5m 6m
PHY 231

13. A rolling coin 0=18 rad/s =-1.80 rad/s l d d=0.02 m
For how long does the coin roll?
What is the average angular velocity?
c) How far (l)does the coin roll before coming to rest?
PHY 231

14. question What is the angular speed about the rotational axis of the
earth for a person standing on the surface?
a)7.3x10-5 rad/s
b)3.6x10-5 rad/s
c)6.28x10-5 rad/s
d)3.14x10-5 rad/s
e) ????
PHY 231

15. question peddles A boy is riding his bike.
If the front gear is rotating
with linear velocity v1 and
angular velocity 1 then
the rear gear has a linear
velocity ??????? v1 and
angular velocity ???????
1. The front gear is larger
in radius than the rear gear.
rear
gear
front
gear
rear wheel
equal to, equal to
equal to, larger than
larger than, larger than
smaller than, larger than
smaller than, equal to
PHY 231

16. gears Next quiz will be like this: bring calculator
If 1=3 rad/s, how fast
Is the bike going?
b) What if r1=0.1 m ?
r3=0.7 m
r1=0.3
r2=0.15 b)
PHY 231