Physics 1D03 - Lecture 10 1

Circular MotionCircular Motion

• Newton’s Second Law and circular motion

Serway and Jewett 6.1, 6.2

Physics 1D03 - Lecture 10 2

Review: Circular Motion Kinematics

has components a

direction in change from , ii)

of change of rate , i)

2

r

va

dt

vda

c

t

speed

center tangential component,

radial component,

ta

ca

a

Physics 1D03 - Lecture 10 3

Particle dynamics : nothing new

• There is no “centrifugal force”• • has a radial component as

well as (perhaps) a tangential component

am

forces) (real a

Centrifugal Force

Centrifugal force is a fictitious force – it is theresult of you being in a non-inertial (accelerating) frame (see Sect 7.5).

Physics 1D03 - Lecture 10 4

Example: Pendulum

Calculate the tension in the string when the pendulum is at the lowest point in the swing.

Given : mass m, length L, and speed at the lowest point.

ov

L

mm

Physics 1D03 - Lecture 10 5

Non-Uniform Circular Motion

Suppose a pendulum is moving fast enough that it swings in a complete vertical circle. Assume we know the mass m, length l, and the speeds at each point.

How do we calculate the radial and tangential accelerations, and the tension in the string?

Note: speed changes in this case because of the gravitational acceleration. m

1

l

2

3

Physics 1D03 - Lecture 10 6

Concept Quiz

The earth is not exactly spherical, so the gravitational field g depends on latitude. The rotation of the earth also affects the measurement of “weight.”

A physicist owns a bathroom scale which reads in newtons. He travels to the North Pole, where the scale reads 978 N when he stands on it. If the earth were to spin twice as fast, what would the bathroom scale read at the pole?

a) 978 N

b) less than 978 N

c) greater than 978 N

rotation

Physics 1D03 - Lecture 10 7

Concept Quiz

The earth is not exactly spherical, so the gravitational field g depends on latitude. The rotation of the earth also affects the measurement of “weight.”

The same physicist travels with his bathroom scale to the equator, where the scale reads 978 N when he stands on it. The gravitational force on him at the equator is:

a) equal to 978 N

b) less than 978 N

c) greater than 978 N

rotation

Physics 1D03 - Lecture 10 8

Example : How fast can the car go without sliding?

r

a

v

sf

Friction of the road on the tires provides the force needed to keep the car traveling in a circle.

If the road is icy (no friction) the car travels in a straight line.

Physics 1D03 - Lecture 10 9

Designing a Road

Roads are “banked” – tilted from side to side on curves – to allow cars to travel at higher speeds without sliding off.

Q: At what speed can the car follow the road with no friction?

Q: What does the free-body diagram look like at other speeds?

r

r

Physics 1D03 - Lecture 10 10

Example:

Calculate the speed at which the car can negotiate the curve without friction. Assume constant speed.

Free-body diagram:

- Two forces: N and gravity

- is horizontal, since the circular path is horizontal.

- the horizontal component of N is the “centripetal” force

a

a

N

gm

Physics 1D03 - Lecture 10 11

a

Solution:

tan rgv

y

x

N

mg