Tangential velocity measures the number of meters the object covers each second. Angular velocity measures the number of radians the object covers each second.
Tangential velocity = (distance in meters) ÷ (time in seconds)
Angular velocity = (angle in radians) ÷ (time in seconds)
1. The moon orbits the earth every 29 days. Find its angular displacement and velocity.
The moon moves around the earth 1 time in 29 days. So, the moon moves 1 circumference in 29 days.
The angular displacement (distance) is (2 * π) radians.
Angular velocity = (2 * π) ÷ (time
Time in seconds = 29 days * 24 hr/day * 60 min/hr * 60 sec/ min.
Angular velocity = (2 * π) ÷ (29 * 24 * 60 * 60)
2. Explain why all points on a spinning object rotate with the same angular velocity but not the same tangential velocity.
If you rotate with your arms extended, your hands are moving farther than your elbows. The radius of the circle in which your hands are moving is greater than the radius of the circle in which your elbows are moving. So, the circumference of the circle in which your hands are moving is greater than the circumference of the circle in which your elbows are moving. You hands and elbow rotate at the same speed, so, their angular velocity is the same. But tangential velocity of your hands is greater than the tangential velocity of your elbows.
The point at the center of your head only rotates. This point has no tangential velocity, only angular velocity.
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