Your roommate is working on his bicycle and has the bike upside down. He spins the 52.0 cm-diameter wheel,?

and you notice that a pebble stuck in the tread goes by three times every second.

1) What is the pebble’s speed?

2)What is the pebble’s acceleration?

Answer:

This is the Best Answer for Your roommate is working on his bicycle and has the bike upside down. He spins the 52.0 cm-diameter wheel,?

Frequency of the pebble is f = 3 Hz.

angular velocity ω= 2π f. = 6π

Linear speed or velocity v = r ω = [0.52/2]*6π = 4.90m/s

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Acceleration = v^2 /r = 4.9^2 / 0.26 = 92.3 m/s^2 toward the center of the wheel.

Circumference of the wheel = 0.52 x pi = 1.633 metres (need the distance in metres for the later calculations)

This passes 3 times per second so the pebble travels 1.633 x 3 metres every second = 4.899 m/s

so the pebbles speed is 4.899 m/s

Now I am assuming this is a circular motion problem, so the acceleration the question is looking for is the acceleration due to the circular motion

This is given by acceleration = speed x speed /radius

a = 4.899 x 4.899 / 0.26 note that 0.26 is the radius which is half the diameter

a = 92.308 m/s/s the direction of the pebbles acceleration is towards the centre of the wheel.

I am ignoring any acceleration due to gravity.

1) Use 52.0 cm diameter to find the circumference of the wheel.

speed = distance/time = (3 x circumference)/second

2) Acceleration is change in velocity (speed with a direction), so if you are working with direction, then you would have to calculate the change in direction to get the velocity.

However, if direction is not important, then speed is not changing therefore velocity is zero.

This is the Correct Answer for Your roommate is working on his bicycle and has the bike upside down. He spins the 52.0 cm-diameter wheel?