2. Rolling Motion

3. Rolling Motion
If we separate the rotational motion from the linear motion, we find that speed of a point on the outer edge of the wheel due to rotation is the same as the linear speed of the whole wheel.

4. But these are both happening at the same time…
Rolling Motion
If we separate the rotational motion from the linear motion, we find that speed of a point on the outer edge of the wheel due to rotation is the same as the linear speed of the whole wheel.
But these are both happening at the same time…

5. Rolling Motion
Add them together…

6. A car with tires of radius 31 cm drives on the highway at 65 mph (29
A car with tires of radius 31 cm drives on the highway at 65 mph (29.1 m/s).
(a) What is the angular speed of the tires?

7. A car with tires of radius 31 cm drives on the highway at 65 mph (29
A car with tires of radius 31 cm drives on the highway at 65 mph (29.1 m/s).
(a) What is the angular speed of the tires?
(b) What is the linear speed of the tops of the tires?

8. The Wheel!

9. Rotational Kinetic Energy

10. Rotational Kinetic Energy
I = “Moment of Inertia”
for a single point mass

11. Moment of Inertia for an extended object

12. for particular geometric shapes
Moments of Inertia
for particular geometric shapes
(Handouts!)

13. They both have the same moment of inertia.
Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold. Which one has the bigger moment of inertia about an axis through its center?
Solid aluminum
Hollow gold
They both have the same moment of inertia.
same mass & radius
solid
hollow
Answer: B

14. Two spheres have the same radius and equal mass
Two spheres have the same radius and equal mass. One is made of solid aluminum, and the other is made from a hollow shell of gold. If the two spheres rotate with a large angular velocity, what happens to their moments of inertia?
They increase.
They decrease.
They stay the same.
same mass & radius
solid
hollow
Answer: C

15. Two spinning disks have the same mass, but disk 2 has double the radius of disk 1. By what factor is disk 2’s moment of inertia greater than disk 1’s moment of inertia?
Two
Four
The same
Disk 1
Disk 2
Answer: B

16. What is the Moment of Inertia of a rotating axe grinder of mass 17
What is the Moment of Inertia of a rotating axe grinder of mass 17.5 kg and diameter 57.0 cm?

17. What is its rotational kinetic energy if it’s rotating at 255 rpm?
What is the Moment of Inertia of a rotating axe grinder of mass 17.5 kg and diameter 57.0 cm?
What is its rotational kinetic energy if it’s rotating at 255 rpm?

18. Total Kinetic Energy is made up of two parts:
Translational + Rotational

19. What is the total kinetic energy of a steel ball of mass 3
What is the total kinetic energy of a steel ball of mass 3.75 kg and diameter 12.6 cm if it rolls at a speed of 68.8 cm/s?

20. Total Kinetic Energy is made up of two parts:
Translational + Rotational
For an object that’s rolling without slipping, w and v are related…

21. Total Kinetic Energy is made up of two parts:
Translational + Rotational
For an object that’s rolling without slipping, w and v are related…

22. What is the kinetic energy of a basketball of mass 0
What is the kinetic energy of a basketball of mass kg and radius 12.1 cm that rolls without slipping with a speed of 1.33 m/s?

23. Two spinning disks have the same mass, but disk 2 has double the radius of disk 1. If disk 1 is rotating at double the angular velocity of disk 2, by what factor does disk 2’s kinetic energy of rotation exceed that of disk 1?
Two
Four
The same
Disk 1
Disk 2
Answer: B

24. Two spinning disks have the same mass, but disk 2 has double the radius of disk 1. Disk 1 is rotating at double the angular velocity of disk 2, and both are rolling without slipping. By what factor does the total kinetic energy of rotation of disk 2 exceed that of disk 1?
Two
Four
The same
Disk 1
Disk 2
Answer: B