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mathdad

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You are given the rate of rotation of a wheel as well as its radius. For A-C, determine the following:

A. The angular speed, in units of radians/sec.

B. The linear speed, in units of cm/sec, of a point on the circumference of the wheel.

C. The linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference.

I will now post my effort.

Given: 500 rpm; r = 45 cm

Part A

The angular speed formula is w = θ/t.

I know that 1 revolution = 2pi radians.

I need θ.

θ = 500 (2pi radians)

θ = 1,000 pi radians.

w = 1,000 pi radians/sec

Book's answer is [50 pi/3] radians/sec. Something tells me that I needed to convert seconds to minutes. Yes?

Part B

I used the arc length formula, s = θr, as step 1.

s = (1,000 pi radians)(45 cm)

s = 45,000 pi cm = d

The letter d represents the distance in time t in the linear speed formula v = d/t.

v = 45,000 pi cm/sec is my answer.

Book's answer for Part B is 750 pi cm/sec.

Again, I am thinking that the units of conversation needed to be changed. Yes?

Part C

s = θr

s = (1,000 pi radians)(22.5 cm)

The decimal 22.5 came from dividing the radius in half in terms of the instructions for Part C above.

s = 22,500 pi cm = d

v = d/t

v = 22,500 pi cm/sec

Book's answer is 375 pi cm/sec.

A. The angular speed, in units of radians/sec.

B. The linear speed, in units of cm/sec, of a point on the circumference of the wheel.

C. The linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference.

I will now post my effort.

Given: 500 rpm; r = 45 cm

Part A

The angular speed formula is w = θ/t.

I know that 1 revolution = 2pi radians.

I need θ.

θ = 500 (2pi radians)

θ = 1,000 pi radians.

w = 1,000 pi radians/sec

Book's answer is [50 pi/3] radians/sec. Something tells me that I needed to convert seconds to minutes. Yes?

Part B

I used the arc length formula, s = θr, as step 1.

s = (1,000 pi radians)(45 cm)

s = 45,000 pi cm = d

The letter d represents the distance in time t in the linear speed formula v = d/t.

v = 45,000 pi cm/sec is my answer.

Book's answer for Part B is 750 pi cm/sec.

Again, I am thinking that the units of conversation needed to be changed. Yes?

Part C

s = θr

s = (1,000 pi radians)(22.5 cm)

The decimal 22.5 came from dividing the radius in half in terms of the instructions for Part C above.

s = 22,500 pi cm = d

v = d/t

v = 22,500 pi cm/sec

Book's answer is 375 pi cm/sec.

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