Pyshics Homework Help?

I've been struggling a little in pyshics with Circular motion. I was able to do some problems on my skill sheet, but there were two that I couldn't really figure out how to solve. So if you could help get the answers and explain how to solve them, that would be great!

1. A bicycle with a front wheel that is 50 centimeters in diameter and a back wheel that is 74 cm in diameter is moving along with a linear speed of 16 km/hour. Find the angular speed of the wheels in radians/sec and in rpm (rpm)

2. A ball with a radius of 1 centimeter starts rolling down a ramp. The acceleration of the ball is 2 meters/sec^2. A: What is the angular speed of the ball after 1 second? After 3 seconds? B: Convert each answer in 8(a) revolutions per second.

*there are 6.28 radians in a full circle.

Thanks in advance!

1 Answer

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  • 8 years ago
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    1)

    First convert the speed from km/h to m/s

    v = 16 km/h = (16000 m) / (3600 s) = 4.44 m/s

    The circumference of the front wheel is:

    S = 2πR = πD

    S = 3.14 × (0.5 m) = 1.57 m

    The angular speed of the front wheel is:

    ω = v / S

    ω = (4.44 m/s) / (1.57 m) = 2.83 rev/s

    But you need the unit to be rpm, so multiply by 60

    ω = (2.83 × 60) rpm = 169 rpm < - - - - - - - - - angular speed of front wheel in rpm

    The circumference of the back wheel is:

    S = 2πR = πD

    S = 3.14 × (0.74 m) = 2.32 m

    The angular speed of the front wheel is (in rev/s):

    ω = v / S

    ω = (4.44 m/s) / (2.32 m) = 1.91 rev/s

    But you need the unit to be rpm, so multiply by 60

    ω = (1.91 × 60) rpm = 114 rpm < - - - - - - - - - angular speed of back wheel in rpm

    2)

    The circumference of the ball is:

    S = 2πR

    S = 2π×(0.01 m) = 0.0628 m

    The speed of the ball after 1 second is:

    v = (2 m/s²)×(1 s) = 2 m/s

    The angular velocity of the ball is (in rad/s):

    ω = v / R

    ω = (2 m/s) / (0.01 m) = 200 rad/s < - - - angular speed of the ball after 1 s in rad/s

    The speed of the ball after 3 second is:

    v = (2 m/s²)×(3 s) = 6 m/s

    The angular velocity of the ball is (in rad/s):

    ω = v / R

    ω = (6 m/s) / (0.01 m) = 600 rad/s < - - - angular speed of the ball after 3 s in rad/s

    To convert rad/s to rev/s, divide by 2π

    200 rad/s = (200 / 2π) rev/s = 31.8 rev/s < - - angular speed of the ball after 1 s in rev/s

    600 rad/s = (600 / 2π) rev/s = 95.5 rev/s < - - angular speed of the ball after 3 s in rev/s

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