Angular Velocity: Find Theta at t=1 & t=5.5

AI Thread Summary
To find the angular velocities at t = 1 and t = 5.5, the angular position equation theta = 4t - 3t^2 + t^3 must first be differentiated with respect to time. The derivative, which represents angular velocity, is calculated as d(theta)/dt = 4 - 6t + 3t^2. Evaluating this derivative at t = 1 yields an angular velocity of 1, while at t = 5.5, it results in 97.625. The initial approach of dividing the position values by time was incorrect; understanding the relationship between position and velocity through differentiation is essential. Thus, the correct method to find angular velocity involves using calculus to derive the position equation.
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The angular position of a point on the rim of a rotating wheel is given by theta = 4* t - 3* t^2 + t^3, where theta is in radians if t is given in seconds.

find the angular velocities as t = 1 and t = 5.5

i plugged the numbers into the given equation to get 2 and 97.625
then i divided by the time to get 2 and 17.75 but both of these are wrong. what am i forgetting?
 
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You are given a position equation, and you want to find the velocities at certain points in time.. do you know the relationship between position equations and velocity equations? Think calculus
 
ahh derivitive thanks
 
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