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Physics; re-up only; not mine
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Lecture 27: Relating Linear and Angular Kinematics
Lecture Objectives 1. Relate the equations of rotational and translational quantities. 2. Apply the rotational kinematic relations in rotating objects.
Relating linear and angular kinematics
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Relating linear and angular kinematics
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Relating linear and angular kinematics
Relating linear and angular kinematics
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Relating linear and angular kinematics
Sample problem: A discus thrower moves the discus in a circle of radius 80.0cm. At a certain instant, the thrower is spinning at an angular speed of 10.0rad/s and the angular speed is increasing at 50.0rad/s2. at this instant, find the tangential and centripetal components of the acceleration of the discus and the magnitude of the acceleration.
Brown Trafton, Beijing Olympics
Given: r = 0.800m ω = 10.0rad/s α = 50.0rad/s2
Given: r = 0.800m ω = 10.0rad/s α = 50.0rad/s2
For the discus moving in a circular path, the tangential and radial acceleration are:
The magnitude of the acceleration is:
Sample Problem: You are asked to design an airplane propeller to turn at 2400rpm. The forward airspeed of the place is to 75.0m/s and the speed of the tips of the propeller blades through the air must not exceed 270m/s. (a) What is the maximum radius the propeller can have? (b) With this radius, what is the acceleration of the propeller tip?
(a) First convert the required angular velocity ω to rad/s:
To calculate the radius we note the velocities of the plane and the tangential velocity to the velocity at the tip of the propeller:
Therefore if the velocity of the propeller blade (tip) is 75.0m/s, the radius is:
(b) Using the radius r = 1.03m, the centripetal acceleration is:
While the tangential acceleration is zero because the speed is constant. ☺
Seatwork
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Seatwork 1 to 4:
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2πrad = 1rev
Seatwork answers
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Seatwork 1 to 4:
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Seatwork 1 to 4:
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Seatwork 1 to 4: