Rotational Velocity & Acceleration Video Lessons

Concept

Problem: Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second.Part AWhat is the pebble's speed?Express your answer with the appropriate unitsPart BWhat is the pebble's acceleration?Express your answer with the appropriate units.

FREE Expert Solution

Tangential speed:

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega }}}$

Acceleration:

$\overline{){\mathbf{a}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}}$

Part A

Given that the pebble goes by three times per second, the angular speed is given in radians as:

ω = (3)(2π) = 18.85 rad/s

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Problem Details

Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second.

Part A

What is the pebble's speed?