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Circular Motion

The wheels on the bus go round and round, but can you name all the forces in a rotating reference frame? Learn to derive these and more through sheer force of reason in Circular Motion.

Uniform Circular Motion - Advanced

         

A pilot executes uniform speed circular path motion in an airplane. The initial velocity (in \(\text{m/s}\)) of the plane is given by \( v_o = 2200 \hat{i} + 2500 \hat{j}. \) One minute later, the velocity of the plane is \( v = -2200 \hat{i} - 2500 \hat{j}. \) Find the approximate magnitude of the acceleration of the plane.

As shown in the above diagram, a \( 2 \text{ kg} \) ball swings at a constant speed in a horizontal circle at the end of a cord of length \( 10 \text{ m}. \) What is the approximate speed of the ball if the rope makes an angle of \( 30 ^\circ \) with the vertical?

Take gravitational acceleration \( g= 10 \text{ m/s}^2. \)

A car is in uniform circular motion on a flat circular track of radius \( 70 \text{ m}. \) If the coefficient of static friction between the car's wheels and the track is \( 0.5 ,\) approximately how fast can the car move without losing traction with the track?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

A coin is gently placed on a rotating horizontal turntable that is slowly accelerating. The coin's initial distance from the axis of rotation is \( 40 \text{ cm}. \) If the coin starts to slip when the coin's speed is \( 60 \text{ cm/s}, \) what is the approximate coefficient of static friction between the coin and the turntable?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

A particle moves in uniform circular motion on the \(xy\)-plane. When the particle's position is \( (2 \text{ m}, 2 \text{ m} ), \) its velocity is \( -4\hat{i} \text{ m/s} \) and acceleration is \( +1.00 \hat{j} \text{ m/s}^2. \) Calculate the coordinates of the center of rotation.

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