A minute hand is 8 cm, the second hand is 8 cm, and a hour hand is 6 cm. It has

Question

A minute hand is 8 cm, the second hand is 8 cm, and a hour hand is 6 cm. It has xy choods with the origin at the center. If the quanities are vectors, you have to use unit vector notation. Display answers 3-4 decimals.

1. If you are on top of the minute hand, what is the velocity at 2:10 with cm/min units?

2. If I'm on the tip of the hour hand, what is my velocity at 5:40 with cm/min units?

3. What is my acceleration at the tip of the minute hand at 5:45 with cm/min2?

4. Compare the centripetal acceleration I would experience if I sit on the tip of the second hand and the minute hand. Here means calculate a ratio like asec/amin=?

Explanation / Answer

1) As time period is defined as

T = 2pi / w

w = 2 pi / T

w = angular velocity

w = 2(3.14) / 60 min T = time period = 60 min ( for minutes hand)

w = 0.104 rad / min

This is the value of angualr velocity

V = r w

V = 8(0.104) cm / min

V = 0.832 cm / min

2) FOr hour hand

w = 2pi / T = 2(3.14) / 12 hours = 0.0087 rad / min

V = rw = 6cm ( 0.0087) / min = 0.052 rad /min

3) In this case accelration would be the radial or centripetal accelration which is equal to

a = w2x

a =( 0.0087)2 (6 * 60) As S = r (theta) here r = 6cm and theta = 600  and x = S

There are 60 degrees in five hours)

a = 0.0272 cm / min2

4) asec = w2sec Xsec

amin = w2min Xmin

asec / amin = w2sec xsec / w2min xmin

=(6.28 rad/ min)2 / (0..104 rad /min)2

= 3646.3 ( answer)

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