find the angular velocity in radians per minute and linear velocity in inches per minute for a point on the…

find the angular velocity in radians per minute and linear velocity in inches per minute for a point on the edge of a 6.9 - in. - diameter record spinning at 44 rev/min. the angular velocity is 276.5 radians per minute. (simplify your answer. type an integer or decimal rounded to the nearest tenth.) the linear velocity is inches per minute. (simplify your answer. type an integer or decimal rounded to the nearest tenth.)

find the angular velocity in radians per minute and linear velocity in inches per minute for a point on the edge of a 6.9 - in. - diameter record spinning at 44 rev/min. the angular velocity is 276.5 radians per minute. (simplify your answer. type an integer or decimal rounded to the nearest tenth.) the linear velocity is inches per minute. (simplify your answer. type an integer or decimal rounded to the nearest tenth.)

Answer

Explanation:

Step1: Find the radius

Given diameter (d = 6.9) inches. Radius (r=\frac{d}{2}=\frac{6.9}{2}=3.45) inches.

Step2: Recall the formula for linear velocity

The formula for linear velocity (v) is (v = r\omega), where (\omega) is the angular velocity. We know (\omega = 276.5) radians per minute and (r = 3.45) inches. Substitute the values into the formula: (v=3.45\times276.5) [v = 3.45\times276.5=3.45\times(276 + 0.5)=3.45\times276+3.45\times0.5] [3.45\times276=(3 + 0.45)\times276=3\times276+0.45\times276 = 828+124.2=952.2] [3.45\times0.5 = 1.725] [v=952.2+1.725 = 953.925\approx953.9]

Answer:

The linear velocity is (953.9) inches per minute.