A 45 N brick is suspended by a light string over a 2.0 kg pulley. Initially, the pulley is prevented from rotating. The pulley is then released from rest. What is the angular speed of the pulley at the instant it has rotated through 5 radians. The pulley may be considered a solid disk of radius 1.5 m. What is the angular speed of the pulley? I know the answer is 7.33 rad/s but i need to know how they got to this answer.

17.3rad/secs.

Explanation:

Given data:

m = 2.0kg

f = 45N

radius of the disk = 1.5m

Solution:

First we determine the kinetic energy of the the system

= 1/2jw^2 + 1/2m(wR)^2

when the brick falls at wR m/s

= 1/2( j + mR^2)w^2

= 1/2 (1/2MR^2 + mR^2)w^2

Loss in potential energy when the brick drops

= 5rad * 1.5m

= 7.5m

Therefore;

45N * 7.5m = 1/2Iw^2

where;

I = 1/2mr^2

angular speed

w = √4*45*7.5/(2*1.5^2)

= 17.3rad/secs

you cant move and you feel like someones pushing you down onto your bed it can feel like you want to get up but you just can't it can be extremely scary

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s