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Lecture Slides on Rotational Motion | PHYS 110, Study notes of Physics

Material Type: Notes; Professor: Finn; Class: Gen Physics IA Lab; Subject: Physics; University: Siena College; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 08/09/2009

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Chapter 8
Rotational Motion
8-1 Angular Quantities
In purely rotational motion, all
points on the object move in circles
around the axis of rotation (“O”).
All points on a straight line drawn
through the axis move through the
same angle in the same time.
The angle θ in radians is defined:
where l is the arc length.
(8-1a)
Think-Pair-Share
Problem 1: Express the following angle in
radians: (a) 30 degrees, (b) 57 degrees.
Give as numerical values and as fractions
of pi.
8-1 Angular Quantities
Angular displacement:
Average angular velocity:
The instantaneous angular
velocity:
(8-2a)
(8-2b)
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Chapter 8

Rotational Motion

8-1 Angular Quantities

  • In purely rotational motion, all points on the object move in circles around the axis of rotation (“ O ”).
  • All points on a straight line drawn through the axis move through the same angle in the same time.
  • The angle θ in radians is defined: where l is the arc length. (8-1a)

Think-Pair-Share

  • Problem 1: Express the following angle in

radians: (a) 30 degrees, (b) 57 degrees.

Give as numerical values and as fractions

of pi.

8-1 Angular Quantities

  • Angular displacement:
  • Average angular velocity:
  • The instantaneous angular velocity: (8-2a) (8-2b)

8-1 Angular Quantities

The angular acceleration is the rate at which the angular velocity changes with time: The instantaneous acceleration: (8-3a) (8-3b) Think-Pair-Share

  • Problem 4: The blades of a blender rotate

at a rate of 6500 rpm. When the motor is

turned off during operation, the blades

slow to rest in 3.0 s. What is the angular

acceleration as the blades slow down?

8-1 Angular Quantities

Every point on a rotating body has an angular velocity ω and a linear velocity v. They are related: (8-4)

8-1 Angular Quantities

Therefore, objects farther from the axis of rotation will move faster.

8-2 Constant Angular Acceleration

The equations of motion for constant angular acceleration are the same as those for linear motion, with the substitution of the angular quantities for the linear ones. Think-Pair-Share

  • Problem 15: A centrifuge accelerates

uniformly from rest to 15,000 rpm in 220 s.

Through how many revolutions did it turn

in this time?

8-3 Rolling Motion (Without Slipping)

  • Rolling without slipping - static friction
    • wheel contact point is a rest WRT ground
  • The linear speed of the wheel is related to its angular speed:

8-4 Torque

To make an object start rotating, a force is needed; the position and direction of the force matter as well. The perpendicular distance from the axis of rotation to the line along which the force acts is called the lever arm.

8-4 Torque

A longer lever arm is very helpful in rotating objects.

8-4 Torque

  • Torque = rotational analog of force
  • r = distance from point of rotation to point where force is applied
  • F = force perpendicular to r
  • FA applies maximum torque Think-Pair-Share
  • Problem 22: A 55-kg person riding a bike

puts all her weight on each pedal when

climbing a hill. The pedals rotate in a

circle of radius 17 cm. (a) What is the

maximum torque she exerts?

8-5 Rotational Dynamics; Torque and

Rotational Inertia

Knowing that , we see that This is for a single point mass; what about an extended object? As the angular acceleration is the same for the whole object, we can write: (8-11) (8-12)

8-6 Solving Problems in Rotational

Dynamics

  1. Draw a diagram.
  2. Decide what the system comprises.
  3. Draw a free-body diagram for each object under consideration, including all the forces acting on it and where they act.
  4. Find the axis of rotation; calculate the torques around it. 5. Apply Newton’s second law for rotation. If the rotational inertia is not provided, you need to find it before proceeding with this step. 6. Apply Newton’s second law for translation and other laws and principles as needed. 7. Solve. 8. Check your answer for units and correct order of magnitude.

8-6 Solving Problems in Rotational

Dynamics