Circular motion Consider an object moving along the circular trajectory r(t) = ⟨A cos ωt, A sin ωt⟩ , where A and ω are constants.a. Over what time interval [0, T] does the object traverse the circle once?b. Find the velocity and speed of the object. Is the velocity constant in either direction or magnitude? Is the speed constant?c. Find the acceleration of the object.d. How are the position and velocity related? How are the position and acceleration related?e. Sketch the position, velocity, and acceleration vectors at four different points on the trajectory with A = ω = 1.
Circular motion Consider an object moving along the circular trajectory r(t) = ⟨A cos ωt, A sin ωt⟩ , where A and ω are constants.a. Over what time interval [0, T] does the object traverse the circle once?b. Find the velocity and speed of the object. Is the velocity constant in either direction or magnitude? Is the speed constant?c. Find the acceleration of the object.d. How are the position and velocity related? How are the position and acceleration related?e. Sketch the position, velocity, and acceleration vectors at four different points on the trajectory with A = ω = 1.
Circular motion Consider an object moving along the circular trajectory r(t) = ⟨A cos ωt, A sin ωt⟩ , where A and ω are constants.a. Over what time interval [0, T] does the object traverse the circle once?b. Find the velocity and speed of the object. Is the velocity constant in either direction or magnitude? Is the speed constant?c. Find the acceleration of the object.d. How are the position and velocity related? How are the position and acceleration related?e. Sketch the position, velocity, and acceleration vectors at four different points on the trajectory with A = ω = 1.
Circular motion Consider an object moving along the circular trajectory r(t) = ⟨A cos ωt, A sin ωt⟩ , where A and ω are constants. a. Over what time interval [0, T] does the object traverse the circle once? b. Find the velocity and speed of the object. Is the velocity constant in either direction or magnitude? Is the speed constant? c. Find the acceleration of the object. d. How are the position and velocity related? How are the position and acceleration related? e. Sketch the position, velocity, and acceleration vectors at four different points on the trajectory with A = ω = 1.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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