The angular velocity of a rotating body is given by the derivative of the angle of rotation with respect to time.

Given the equation θ = 2t³ + 3t² + 10, we can find the angular velocity by taking the derivative of this equation with respect to time (t).

The derivative of 2t³ with respect to t is 6t².
The derivative of 3t² with respect to t is 6t.
The derivative of 10 with respect to t is 0.

So, the angular velocity (ω) is given by the equation ω = 6t² + 6t.

To find the angular velocity after 4 seconds, we substitute t = 4 into this equation:

ω = 6(4)² + 6(4) = 96 + 24 = 120 rad/s.

So, the angular velocity of the rotating body after 4 seconds is 120 rad/s.

Question

The angular velocity of a rotating body is given by the derivative of the angle of rotation with respect to time.

Given the equation θ = 2t³ + 3t² + 10, we can find the angular velocity by taking the derivative of this equation with respect to time (t).

The derivative of 2t³ with respect to t is 6t².
The derivative of 3t² with respect to t is 6t.
The derivative of 10 with respect to t is 0.

So, the angular velocity (ω) is given by the equation ω = 6t² + 6t.

To find the angular velocity after 4 seconds, we substitute t = 4 into this equation:

ω = 6(4)² + 6(4) = 96 + 24 = 120 rad/s.

So, the angular velocity of the rotating body after 4 seconds is 120 rad/s.

Knowee AI · Accepted Answer

The angular velocity of a rotating body is given by the derivative of the angle of rotation with respect to time.

Given the equation θ = 2t³ + 3t² + 10, we can find the angular velocity by taking the derivative of this equation with respect to time (t).

The derivative of 2t³ with respect to t is 6t².
The derivative of 3t² with respect to t is 6t.
The derivative of 10 with respect to t is 0.

So, the angular velocity (ω) is given by the equation ω = 6t² + 6t.

To find the angular velocity after 4 seconds, we substitute t = 4 into this equation:

ω = 6(4)² + 6(4) = 96 + 24 = 120 rad/s.

So, the angular velocity of the rotating body after 4 seconds is 120 rad/s.

The relation between the angle of rotation (θ) in radians and time (t) in secondsof a rotating body is given by the equation. θ = 2t3 + 3t2 + 10. Interpret the angularvelocity after 4 seconds.