Electric Rotating Turntable
December 6th, 2009
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Electric Rotating Turntable
PHYSICS HELP! Rotational Acceleration?
I've managed to solve all other parts of this problem, but I can't figure out how to get the magnitude of the acceleration. I've tried it several different ways and I keep getting it wrong. Would someone mind telling me how I should go about solving this problem???
An electric turntable 0.730 m. in diameter is rotating about a fixed axis with an initial angular velocity of 0.240 rev/s. The angular acceleration is 0.911 rev/s^2. If the angular velocity after a time of 0.199 s is w=0.421 rev/s and the tangential speed of a point on the tip of the blade at the same time is 0.966 m/s, what is the magnitude of the resultant acceleration of a point on the tip of the blade at time = 0.199 s?
First you need to convert everything to radians:
α = (0.911 rev/s²)(2π rad/rev) = 5.724 rad/s²
ω = (0.421 rev/s)(2π rad/rev) = 2.645 rad/s
The tangential acceleration of the point is just
a_t = αr
a_t = (5.724 rad/s²)(0.73 m / 2) = 2.089 m/s²
And the normal acceleration is given by
a_n = rω²
a_n = (0.73 m / 2)(2.645 rad/s)² = 2.554 m/s²
To find the magnitude, combine the two perpendicular vectors with they Pythagorean theorem:
a = √(a_t² + a_n²)
a = √[ (2.089 m/s²)² + (2.554 m/s²)² ]
a = 3.30 m/s²
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