Find the linear speed v for each of the following.

Question

the tip of the minute hand of a clock, if the hand is 7 cm long

Accepted Answer

Welcome back. I am so glad you're here. We're told that a large clock is displayed at a market in Barcelona, Spain. Calculate the linear speed V of the tip of its minute hand. If the hand has a length of 50 centimeters, our answer choices are answer choice. A five pi divided by six centimeters per minute. Answer choice. B six pi divided by five centimeters per minute. Answer choice. C five pi divided by three centimeters per minute and answer choice D three pi divided by two centimeters per minute. All right. So we are looking for linear speed V and we recall from previous lessons that for linear speed, we have a formula where linear speed equals our radius multiplied by Omega the angular speed. And we have the radius here. The radius of our clock face is 50 centimeters. R equals 50 centimeters. But what about our angular speed? What about Omega? Well, Omega is expressed in terms of the divided by t it's our radians per unit of time. And we're talking about in one revolution around this clock face, the tip travels to pie radiance. But how long does that take? Well, it's going to take that minute hand, 60 minutes. And I am choosing minutes for the unit of time because all of our answer choices have minutes as their unit of time. So there's our omega now to find V we just multiply r 50 centimeters. Buy Omega two P radians divided by 60 minutes. And now we can just multiply straight across 50 multiplied by two. Pi is 100 pi that's divided by, we have 60 for the numbers. And then for our units in the numerator, we have centimeters multiplied by radiance all divided by minutes. We can simplify the 100 pi divided by 60. They're both divisible by 20. So that simplifies to be five pi divided by three. Now, in terms of our units, we're talking about linear speed and linear speed is expressed in terms of distance divided by time. So we can disregard our radiance unit in our answer. And it's just going to be centimeters per minute. And that is our linear speed. Five pi divided by three centimeters per minute. We look at our answer choices and that matches with answer choice. C well done. We'll catch you on the next one.

Find the linear speed v for each of the following.

the tip of the minute hand of a clock, if the hand is 7 cm long

Key Concepts

Angular Velocity

Relationship Between Linear and Angular Velocity

Radius of Rotation

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