# Angular velocity-acceleration

#### chino109

The clock has a diameter of 30 cm. It has an hour, minute and second hands.
1. there is a speck of dust on the second hand, Where is the speck located if its velocity is: (a) the fastest it could be (b) the slowest it could be

2. In rad/s, what is the angular velocity of the second hand?

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A merry-go-round makes 2 complete rotations in 9.6 s. What is its angular velocity?

Is this average or instantaneous? Explain.

A car increases speed from 2pi/3 rad/s to 3pi/2 rad/s in 5.0 s. What is the angular acceleration of the car?

Thanks for the help(Worried)

#### physicsquest

PHF Helper
The clock has a diameter of 30 cm. It has an hour, minute and second hands.
1. there is a speck of dust on the second hand, Where is the speck located if its velocity is: (a) the fastest it could be (b) the slowest it could be

The fastest would be at the edgae and the slowest at the centre (0) as far as linear velocity is concerned. The angular vel is the same everywhere except at the centre

#### physicsquest

PHF Helper
2. In rad/s, what is the angular velocity of the second hand?

___________________
A merry-go-round makes 2 complete rotations in 9.6 s. What is its angular velocity?

Is this average or instantaneous? Explain.

It covers 2pi rad in 60 sec ( 1 min) so ang vel = 2pii/60 = pi/30 rad/sec.

The ang vel of the merrygo round is 2 x 2pi/ 9.6 = 0.416 rad/ sec.

This is average from the given info since itcould have slowed down or speeded up in between unlike the case of the clock where it the avg and inst ang vel are the same.

#### physicsquest

PHF Helper
A car increases speed from 2pi/3 rad/s to 3pi/2 rad/s in 5.0 s. What is the angular acceleration of the car?

Ang acln = rate of change of ang vel = (3-2)pi / 5 rad/sec/sec