Rotational Dynamics

Sep 06, 2012

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Rotational Dynamics

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1. Rotational Dynamics

2. Radian measure compared to degree measure 1 radian = angle of rotation where the arc length of rotation = radius of the circle

Rotational Dynamics Continued

Rotational Dynamics Continued. Translation-Rotation Analogues & Connections. Translation Rotation Displacement x θ Velocity v ω Acceleration a α Force (Torque) F τ Mass (moment of inertia) m I Newton’s 2 nd Law ∑ F = ma ∑τ = I α

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Rotational Dynamics I

When we studied linear motion we started with the description of linear motion which we called kinematics.? From there we went on to dynamics which provided the reason for the motion, i.e. the cause or influence. In a similar fashion we introduced rotational kinematics relating t, q, w, and a.? Cont

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Rotational Dynamics

Rotational Dynamics. When you apply a force to a rigid body (i.e. one that maintains its form with no internal disruption) at a distance from an axis, the torque you create will cause ____. a. In the translational world, F=ma . In the rotational world, ___=___ ___. t. I. a.

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Rotational Dynamics

Rotational Dynamics. angle of rotation (rads). angular velocity (rad/s). angular acceleration (rad/s 2 ). torque (N m). moment of inertia (kg m 2 ). Newton’s 2 nd Law. Kinetic Energy (joules J). IC. (Conservation of Mechanical Energy). Tod. Torque and Moment of Inertia.

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Rotational Dynamics

Rotational Dynamics. Chapter 8 Section 3. Torque Direction. A net positive torque causes an object to rotate counterclockwise. A net negative torque causes an object to rotate clockwise. +. -. Newton’s Second Law for Rotation. Σ T = I α

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Rotational dynamics

Rotational dynamics. Chapter 8. Masses. Up ‘til now, we have assumed that all masses are essentially points in space. From this point onwards, we will treat all objects as extended . Rotation. We established earlier that centripetal force causes circular motion.

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Rotational Equilibrium and Rotational Dynamics

Rotational Equilibrium and Rotational Dynamics. Read introduction page 226

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Rotational Dynamics

Racquetball Striking a Wall. Rotational Dynamics. General Physics I Mechanics Physics 140. Stewart Hall. Mt. Etna. The “rotating effect” of a force is greater, if the force is greater The “rotating effect” of a force is greater, if the force is applied further from the axis of rotation

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Rotational Dynamics

Lecture 15. Rotational Dynamics. Reading and Review. Moment of Inertia. The moment of inertia I:. The total kinetic energy of a rolling object is the sum of its linear and rotational kinetic energies:. Rolling Down.

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Rotational Dynamics

Rotational Dynamics. Torque & Rotational Kinematics. Presentation 2003 R. McDermott. Torque. Torque is the rotational equivalent of force Force tends to cause linear acceleration Torque tends to cause rotational acceleration Occurs when forces do not meet at a point (non-concurrent forces).

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Rotational Dynamics

Rotational Dynamics. Causes of rotational motion! Analogies between linear & rotational motion continue. Newton’s 3 Laws are still valid! But, here we write them using rotational language and notation. Translational-Rotational Analogues Continue!. ANALOGUES

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Rotational Dynamics

Rotational Dynamics. Chapter 9. Expectations. After Chapter 9, students will : calculate torques produced by forces recognize the condition of complete equilibrium calculate the location of the center of gravity of a collection of objects

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Rotational Dynamics

Rotational Dynamics. Radian measure compared to degree measure. 1 radian = angle of rotation where the arc length of rotation = radius of the circle. 1 rad = about 57 ˚ 2 π rad = 360˚. Rotational displacement. Change in the angle of rotation Symbol is θ (theta), unit is rads

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Rotational Dynamics

Rotational Dynamics. Just as the description of rotary motion is analogous to translational motion, the causes of angular motion are analogous to the causes of translational motion:. Newton’s Second Law. Translational Motion F = ma.

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Rotational Dynamics

Rotational Dynamics. The action of forces and torques on rigid object: Which object would be best to put a screw into a very dense, hard wood? A B= either C. Torque = Amount of Force x Lever Arm T = F L. Nm = N x m.

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Rotational Dynamics

Rotational Dynamics. 8.3. Net positive torque, counterclockwise acceleration. Net negative torque, clockwise acceleration. Newton’s Second Law of Rotation. When net torque is zero: Object rotates at constant velocity, Or if object at rest, object does not rotate. Momentum.

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Rotational Equilibrium and Rotational Dynamics

Physics 2053. Lecture Notes. Rotational Equilibrium and Rotational Dynamics. Rotational Motion 1 of 25. Rotational Equilibrium and Dynamics. Topics. 9-01 Torque. 8-02 Torque and the Conditions for Equilibrium. 8-03 Center of Gravity. 8-04 Examples of Objects in Equilibrium.

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Rotational Dynamics

Rotational Dynamics. Moment of Inertia. The angular acceleration of a rotating rigid body is proportional to the net applied torque :. a is inversely proportional to a property of the body called its moment of inertia. Newton’s second law for rotation: SI unit: kg . m 2.

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Rotational Dynamics

Rotational Dynamics. October 24, 2005. 60. w. 5. 0. Bonnie. Klyde. 0. Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde’s angular velocity is:.

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Rotational Motion – Dynamics

Rotational Motion – Dynamics. AP Physics. Rotational Objects roll Inertia Torque Angular Acceleration Rotational K Angular Momentum. Translational Objects slide Mass Force Acceleration Kinetic Energy Momentum. Rotational and Translational Equalities. Torque.

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Rotational Equilibrium and Rotational Dynamics

Rotational Equilibrium and Rotational Dynamics. Read introduction page 226

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Rotational Dynamics

Rotational Dynamics. Chapter 11. Important quantities. Moment of inertia, I. Used in t =I a . So, I divided by time-squared has units of force times distance (torque). Total linear momentum is the sum of the individual momenta. Center-of-mass is a distance. Has to have units of meters.

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