Physics 10 Kinematics Rotational Motion Presentation

Changing angular velocity means that an angular
acceleration is occurring.

DEFINITION OF AVERAGE ANGULAR ACCELERATION

SI Unit of Angular acceleration: radian per second squared (rad/s2)

Example 4 A Jet Revving Its Engines

As seen from the front of the
engine, the fan blades are
rotating with an angular
speed of -110 rad/s. As the
plane takes off, the angular
velocity of the blades reaches
-330 rad/s in a time of 14 s.

Find the angular acceleration, assuming it to
be constant.

Example 6 A Helicopter Blade

A helicopter blade has an angular speed of 6.50 rev/s and an
angular acceleration of 1.30 rev/s2.
For point 1 on the blade, find
the magnitude of (a) the
tangential speed and (b) the
tangential acceleration.

The tangential speed of a
point on the outer edge of
the tire is equal to the speed
of the car over the ground.

Example 8 An Accelerating Car

Starting from rest, the car accelerates
for 20.0 s with a constant linear
acceleration of 0.800 m/s2. The
radius of the tires is 0.330 m.

What is the angle through which
each wheel has rotated?

DEFINITION OF UNIFORM CIRCULAR MOTION

Uniform circular motion is the motion of an object
traveling at a constant speed on a circular path.

Circular Motion

Example 1: Speed of a tire

The wheel of a car has a radius of 0.29m and it being rotated at 830 revolutions per minute on a tire-balancing machine. Determine the speed at which the outer edge of the wheel is
moving.

Circular Motion

Centripetal Acceleration

In uniform circular motion, the speed is constant, but the
direction of the velocity vector is not constant.

Centripetal Acceleration

Due to the properties of similar triangles

Centripetal Acceleration

Conceptual Example 2: Which Way Will the Object Go?

An object is in uniform circular
motion. At point O it is released
from its circular path. Does the
object move along the straight
path between O and A or along
the circular arc between points
O and P ?

Centripetal Acceleration

An object of m=1kg rotates vertically with speed 10m/s as shown. If the speed
Is 10m/s and r=.5m calculate the tension at the highest and lowest point.

Centripetal Acceleration

On Top:

= 200N

On Bottom:

= 210N

Gravitation Force

There is only one speed that a satellite can have if the
satellite is to remain in an orbit with a fixed radius.

Determine the speed of the Hubble Space Telescope orbiting
at a height of 598 km above the earth’s surface.

Conceptual Example 12: Apparent Weightlessness and Free Fall

In each case, what is the weight recorded by the scale?

At what speed must the surface of the space station move
so that the astronaut experiences a push on his feet equal to
his weight on earth? The radius is 1700 m.

Using the information provided, find the magnitude and
direction of the force on the 2kg mass.

Gravitational Potential

For objects at or near the Earth’s surface

General Equation for Gravitational Potential

We set the gravitational energy to be =0 for r at infinity

So now we can apply this to the Conservation of Energy

The graph below shows a plot of the potential energy vs. distance