The relationship between linear speed v and angular speed omega for a body moving in a circle of radius r is
Correct answer: C. v equals r omega
- A. v equals omega divided by r
- B. v equals r divided by omega
- C. v equals r omega
- D. v equals r squared omega
Explanation
In one second the body sweeps an angle omega, covering an arc of length r omega, so the linear speed is r omega with omega in radians per second. This is why two points on a rotating disc share the same angular speed while the outer point moves faster in a straight line sense. The same relationship links angular and linear acceleration as a equals r alpha.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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