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Please help with these questions What is the angular and linear velocity of the

ID: 779245 • Letter: P

Question

Please help with these questions

What is the angular and linear velocity of the second hand of a clock with a diameter of 50. cm? Minute hand? Hour hand? Convert the following first to angular velocity and then to tangential velocity: 4) 5) A disc with a diameter of 10.0 cm spinning at 5000. RPM (Revolutions per minutes) A baton with a length of 0.50 m is spun about its center at 200. RPM. a. b. 6) What is the period of rotation for each of the following? a. r-0.125, 6.0 - b. r-25, 15 c. r0.50, 950° per second

Explanation / Answer

4) diameter = 50 cm, radius = 25 cm

The second-hand takes 60 sec to complete one round or 2 pi radians. Therefore angular velocity is given as 2pi/60

For second hand, angular velocity = 2pi/60 = 0.104 rad/s

Linear velocity = angular velocity x radius = 0.104 x 25 = 2.6 cm/s

Similarly, the minute hand takes 60 minutes or 3600 sec to complete one round or 2pi radians

For minute hand, angular velocity = 2pi/3600 = 0.00174 rad/s

Linear velocity = angular velocity x radius = 0.00174 x 25 = 0.0435 cm/s

For hour hand, angular velocity = 2pi/(12x3600) = 1.45e-4 rad/s

Linear velocity = angular velocity x radius = 1.45e-4 x 25 = 3.6e-3 cm/s

5)

a. Diameter = 10 cm, radius = 5cm, RPM = 5000

Angular velocity = 2pi x (rpm/60) = 2 x 3.14 x (5000/60) = 523.33 rad/s

Tangential velocity = r x angular velocity = 5 x 523.33 = 2616.65 cm/s

b. Length = 0.5 m, radius becomes 0.25 m if rotated at its centre, RPM = 200

Angular velocity = 2pi x (rpm/60) = 2 x 3.14 x (200/60) = 20.93 rad/s

Tangential velocity = r x angular velocity = 0.25 x 20.93 = 5.2325 cm/s

6)

a. angular velocity = linear velocity/ radius = 6/0.125 = 48 rad/s

period = 2pi/angular velocity = 0.13 sec

b. angular velocity = linear velocity/ radius = 15/2.5 = 6 rad/s

period = 2pi/angular velocity = 1.04 sec

c. given 950 deg/s = 16.57 rad/s (angular velocity)

Time period = 2pi/angular velocity = 0.37 sec