Skateboarder on a ramp| Physics

A skateboarder starts up a 1.0-m-high, 30° ramp at a speed of 6.9 m/s. The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air.

A) How far from the end of the ramp does the skateboarder touch down?

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Angular Acceleration| Circular Motion| Physics

Your car tire is rotating at 4.0 rev/s when suddenly you press down hard on the accelerator. After traveling 300 m, the tire’s rotation has increased to 6.5 rev/s . The radius of the tire is 32 cm.

A) What was the tire’s angular acceleration? Give your answer in rad/s²?

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Revolutions from angular velocity vs time graph| Circular Motion| Physics


The figure shows the angular-velocity-versus-time graph for a particle moving in a circle.

How many revolutions does the object make during the first 4.0 s?


Solution:

Part A

The total number of radians made by the object is the area under the graph. Based on the given graph, the total number of radians is 

\displaystyle \theta _{rad}=60\:radians

Convert this to revolutions, knowing that 2π radians is equal to 1 revolution. 

\displaystyle  revolutions=60\:rad\times \frac{1\:rev}{2\pi }=\frac{60}{2\pi }rev=9.5\:rev