Rotational motion

Think of curves, loops, circles and circular motion now!

A merry-go-round is accelerated at a constant rate of 0.005 rev/s2, starting from rest.What is its rotational velocity at the end of 1 min?

= 0.005 rev/s2

0 = 0t = 60 s

= 0 + t = 0 + (0.005 rev/s2)(60 s) = 0.30 rev/s

a) 0.005 rev/sb) 0.03 rev/sc) 0.05 rev/sd) 0.30 rev/s

How many revolutions does the merry-go-round make in 1 minute?

= 0.005 rev/s2

0 = 0t = 60 s, = 0.30 rev/s

= 0t + 1/2 t2

= 0 + 1/2 (0.005 rev/s2)(60 s)2

= 9 rev

a) 1.5 revb) 3.0 revc) 9.0 revd) 18.0 rev

On a merry-go-round, who is moving faster:the boy, or the girl?

v = 0

v = 2 vcm

v = vcm

Very blurred because at that point:

The image is sharper at the bottom because there:

Rolling motion of a wheel as a combination of purely rotational motion and purely translational motion.

(a) The purely rotational motion: all points on the wheel move with the same angular speed ω. Points on the outside edge of the wheel all move with the same linear speed v = vcm.

(b) The purely translational motion: all points on the wheel move to the right with the same linear velocity v as the center of the wheel.

(c) The rolling motion of the wheel is the combination of (a) and (b).

ROTATIONAL LINEAR

COMBINATION

vi

vf

Δs

rr

Δθ

Magnitude of vi = vf , so:

r

s

v

vr

s

v

v

sr

vv s

r

vv

t

va

t

va

ΔvΔθ

vf

vi

Centripetal acceleration

We know that:

Back to the equation above:

Isolating Δv:

Centripetal acceleration

An object moves in a circular path with constant speed v. Which of the following statements is true concerning the object?

1. Its velocity is constant, but its acceleration is changing.

2. Its acceleration is constant, but its velocity is changing.

3. Both its velocity and acceleration are changing.

4. Its velocity and acceleration remain constant.

Quick Quiz

Centripetal force is NOT a new type of force.

It is just another name we give to the net force that is causing the circular motion.

r

vmFc

2

Without a centripetal force, an object in motion continues along a straight-line path.

With a centripetal force, an object in motion will be

accelerated and change its direction.

Objects want to stay naturally in a straight line motion, unless a centripetal force acts upon them.

What’s the force playing the role of a centripetal force here?

Gravitational forces

What’s the force playing the role of a centripetal force here?

stringTension force

What’s the force playing the role of a centripetal force here?

Frictional forces

Centripetal force in a rollercoaster: an interplay between NORMAL force and force of GRAVITY.

What’s the force playing the role of a centripetal force here?

Spring force

F = -kx

Centripetal is the real force in an inertial frame of reference.

But if you are rotating, you need to change the equations to adapt to your rotational frame of reference, then and only then, there will actually be a term called “centrifugal force”.

But be careful. In most cases, to solve most problems in Physics, you are in an inertial frame of reference, and in this frame, centrifugal force becomes a fictitious force, not real, non-existent.