Classical Mechanics

# 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 $$-4\hat{x} \text{ m/s}$$ and acceleration is $$+1.00 \hat{y} \text{ m/s}^2.$$

Calculate the coordinates of the center of rotation.

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