Monday, January 5, 2015 Objective: Students will investigate the relationship between displacement and rotational motion of objects. Homework: None! Bellringer.

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Presentation transcript:

Monday, January 5, 2015 Objective: Students will investigate the relationship between displacement and rotational motion of objects. Homework: None! Bellringer Answer Choices: 1. a AU b AU c AU d AU 2. f AU g AU h AU j AU Welcome Back!

Think & Write What does it mean for something to revolve? What does it mean for something to rotate? Give an example of each.

Turn & Talk Share what you wrote with your neighbor. Do you both agree? Disagree? Be prepared to share out.

Rotational Motion Move to groups. Read the passage at the top of your handout. Work through the first short answer question, and the investigation, as written. When you are done, let Ms. Kline know, before you move on.

Unit Circle Radian: the angle for which the length of a circular arc is equal to the radius of the circle. 2 pi radians = radian = revolution = 2 pi radians = circumference of the circle

Unit Circle If we cant to know an arc length, we can use the following equation:

Back to Your Model Convert your value into radians. Complete the practice problems on the worksheet.

3-2-1 What are 3 things you learned about rotational motion? What are 2 things you want to know? What is 1 question you have about the process, or in general?

Tuesday, January 6, 2015 Objective: Students practice calculating arc length and displacement in practice problems. Bellringer Answer Choices: 3. a.Both points are unstable, and L1 is farther away from the Sun. b.Both points are unstable, and L2 is farther away from the Earth. c.Both points are unstable and are on opposite sides of the Earth. d.Both points are stable, and L2 is farther away from the sun. 4. f.less than the distance from the Sun to Mercury. g.between the distance from the Sun to Venus and the distance from the Sun to Earth. h.greater than the distance from the Sun to Mars. j.between 1 AU and the distance from the Sun to Mars. Homework: Reading Due Thursday!

Reading Questions Answer the following questions in complete sentences (2-3 per question): – How is the planet mentioned in the article like Earth? – Could humans live on this planet? Why or why not? – How is this planet similar and different from other Earth-like planets that have been found?

Back to Yesterday What is a radian? How is a radian related to degrees? To the unit circle?

Unit Circle Radian: the angle for which the length of a circular arc is equal to the radius of the circle. 2 pi radians = radian = revolution = 2 pi radians = circumference of the circle

Friday, January 9, 2015 Objective: Students will differentiate between angular and linear velocity and calculate both velocities from examples. Homework: Practice problems not completed in class. Bellringer Answer Choices: 5. a.I only b.II only c.III only d.II and III only 6. a. Mercury b. Venus c.Earth d.Mars Reading due today!

Monday, January 12, 2015 Objective: Students will differentiate between angular and linear velocity and calculate both velocities from examples. Homework: Practice problems not completed in class. Bellringer Answer Choices: 7. f.Mercury g.Venus h.Earth j.Mars 8. a.collinear Lagrangian points only. b.triangular labrangian points only. c.2 collinear Lagrangian points and 3 triangular Lagrangian points. d.3 collinear Lagrangian points and 2 triangular Lagrangian points. Reading due!

Converting Between Degrees and Radians

Unit Circle Angle measures are given relative to a reference line. That line is usually at 0 0, or 0 radians. – Can be changed! Position is given in radians

Review A fan that is turning at 10 rpm speeds up to 25 rpm. – Convert both speeds to radians per second.

Unit Circle Counterclockwise rotation = positive motion (positive velocity) Clockwise rotation = negative motion (negative velocity)

Circular Motion Terms The point or line that is the center of the circle is the axis of rotation. If the axis of rotation is inside the object, the object is rotating (spinning). If the axis of rotation is outside the object, the object is revolving.

Unit Circle If we want to know an arc length, we can use the following equation:

Practice Problem #1 While riding on a merry-go-round, a child travels through an arc length of 11.5 m. If the merry-go-round has a radius of 4 m, through what angle (theta) does the child travel? Give the angle in radians, degrees, and rotations.

Practice Problem #2 A beetle sits stuck in the tread atop a bicycle wheel with a radius of m. Assuming the wheel turns counterclockwise, what is the angular displacement of the beetle before it is squashed under the wheel? What arc length does the beetle travel through before it is squashed?

Rotational/Angular Velocity Objects moving in a circle also have a rotational or angular velocity, which is the rate angular position changes. Rotational velocity is measured in degrees/second, rotations/minute (rpm), etc. Common symbol,  (Greek letter omega)

Rotational/Angular Velocity Objects moving in a circle also have a rotational or angular velocity, which is the rate angular position changes. Rotational velocity is measured in degrees/second, rotations/minute (rpm), etc. Common symbol,  (Greek letter omega)

Linear/Tangential Velocity Objects moving in a circle still have a linear velocity = distance/time. This is often called tangential velocity, since the direction of the linear velocity is tangent to the circle. v

Rotational/Angular Velocity Rotational velocity = Change in angle time

Tuesday, January 13, 2015 Objective: Students will calculate angular displacement, angular velocity, and tangential velocity. Homework: Practice problems not completed in class. Bellringer Answer Choices: 9. f.L1 and L2 g.L2 and L4 h.L1 and L5 j.L4 and L5 10. a.The Mercury-Sun system b.The Venus-Sun system c.The Earth-Sun system d.The Mars-Sun system Book problems: 65,67,71,75

Linear & Angular Velocity Linear Velocity is distance/time: Angular Velocity is turn/time: Definition: Ex. 55 mph, 6 ft/sec, 27 cm/min, 4.5 m/sec The most common unit is RPM. Ex. 6 rev/min, 360 °/day, 2π rad/hour

Practice Problem #3 A car tire rotates at a constant angular velocity of 3.5 rotations during a time interval of 0.75 s. What is the angular speed of the tire in radians per sec, degrees per sec, and rotations per minute?

Book Practice Problems On page 275, do problems 15-16,18

Linear & Angular Velocity Find the angular velocity in radians per second of a microwave turntable if it turns through an angle of 36° each second.

Linear & Angular Velocity The cable lifting a garage door turns around a pulley at a rate of 20 cm per second. How long will it take to lift the door 2.2 meters?

Acceleration Angular Acceleration is change in angular velocity/change in time: Units: rad/s 2 Definition: Tangential acceleration is the change in tangential velocity Units: m/s 2 Definition: