Chapter 10 Rotational Motion kinetic energy and moment

Chapter 10 Rotational Motion (kinetic energy and moment of inertia)

Radian Vs Degree

Using Radian

Example

Example What is θ in radians and in degrees?

Angular velocity

v and ω The dot goes around the circle of radius r=2 m once every 10 s. What is its v and ω?

Meaning of different variables

Must remember this: Using this you can convert freely among ω, T, f and v.

Period T and frequency f

Example Given r =2 m, T=10 s, find v and ω.

Example Given r =2 m, f = 20 rpm, find v and ω.

Example A car takes 5 minutes to complete one circle on the race track. What is its angular velocity?

Equations of Circular Motion (Must Memorize) y v (x, y) r x

Units

Angular acceleration α

Equations of Motion Linear Circular

Example: Wheel Radius r =2 m Angular acceleration: α=3 rad/s 2 Initial angular velocity ω0=0 rad/s After 5 s, what is the final angular velocity? What angle has the wheel rotated. How far has the wheel rolled on the ground?

Moment of Inertia m 1 m 2 1 m m 3 2 m 5 m r is the distance from the axis of rotation.

Dependence on axis of rotation The moment of inertia will depends on the axis of rotation.

Example 1 To find I, ask yourself: What is the distance r of each mass from the axis of rotation?

Example 2 To find I, ask yourself: What is the distance r of each mass from the axis of rotation?

I for extended objects

Rotational Energy

Example

Example A sphere rolling down from rest. Find velocity at the bottom.

Example

Example (modified) What is the sphere slides down instead?