Classical Mechanics

Circular Motion

Uniform circular motion - advanced

         

A pilot executes uniform speed circular path motion in an airplane. The initial velocity (in m/s\text{m/s}) of the plane is given by vo=2200i^+2500j^. v_o = 2200 \hat{i} + 2500 \hat{j}. One minute later, the velocity of the plane is v=2200i^2500j^. 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 kg 2 \text{ kg} ball swings at a constant speed in a horizontal circle at the end of a cord of length 10 m. 10 \text{ m}. What is the approximate speed of the ball if the rope makes an angle of 30 30 ^\circ with the vertical?

Take gravitational acceleration g=10 m/s2. g= 10 \text{ m/s}^2.

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

The gravitational acceleration is g=10 m/s2. 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 cm. 40 \text{ cm}. If the coin starts to slip when the coin's speed is 60 cm/s, 60 \text{ cm/s}, what is the approximate coefficient of static friction between the coin and the turntable?

The gravitational acceleration is g=10 m/s2. g= 10 \text{ m/s}^2.

A particle moves in uniform circular motion on the xyxy-plane. When the particle's position is (2 m,2 m), (2 \text{ m}, 2 \text{ m} ), its velocity is 4x^ m/s -4\hat{x} \text{ m/s} and acceleration is +1.00y^ m/s2. +1.00 \hat{y} \text{ m/s}^2.

Calculate the coordinates of the center of rotation.

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