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Physics For Scientists & Engineers
Found in: Page 326

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Short Answer

A small object with mass 4.00 kg moves counter-clockwise with constant angular speed 1.50 rad/s in a circle of radius 3.00 m centered at the origin. It starts at the point with position vector 3.00i^ m. It then undergoes an angular displacement of 9.00 rad. (a) What is its new position vector? Use unit-vector notation for all vector answers. (b) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c) What is its velocity? (d) In what direction is it moving? (e) What is its acceleration? (f) Make a sketch of its position, velocity, and acceleration vectors. (g) What total force is exerted on the object?

The new position vector of object is -2.74i^+1.22j^ m.

See the step by step solution

Step by Step Solution

Step 1: Identification of given data

The mass of object is m = 4 kg

The constant angular speed of object is ω=1.50 rad/s

The radius of circle is R = 3m

The angular displacement of object is δ=9 rad

Step 2: Conceptual Explanation

The angular speed of an object is the rate of variation of the angular displacement of the object with time.

Step 3: Determination of new position vector

The angle for the new position vector is given as:

α=δ180°π-360=9 rad180°π rad-360°=156°

The new position vector of object is given as:

r=Rcosαi^+sinαj^=3 mcos156°i^+sin156°j^=-2.74i^+1.22j^ m

Therefore, the new position vector of object is -2.74i^+1.22j^ m .

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