Converting Between Linear & Rotational Video Lessons

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Problem: A particle is moving in a circle of radius 2 meters according to the relation θ = 3t2 + 2t, where θ  is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is (A) 13 m/s (B) 16 m/s (C) 26 m/s (D) 52 m/s (E) 338 m/s 

FREE Expert Solution

This is a calculus problem because we are given a position funtion. The angular position is given in terms of θ. To get the angular velocity function, we need the relationship between angular position and angular velocity.

Motion with Calculus:

θωddtdtα where θ is the position, ω is the angular velocity, and α is angular acceleration.

Power rule of derivation:

ddt(xn)=nxn-1

Relationship between linear and roational:

v=rω

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Problem Details

A particle is moving in a circle of radius 2 meters according to the relation θ = 3t2 + 2t, where θ  is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is 

(A) 13 m/s 

(B) 16 m/s 

(C) 26 m/s 

(D) 52 m/s 

(E) 338 m/s 

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