Question

A wheel is running at a constant speed of 360 r. p. m. At what constant rate, in rad/s, its motion must be retarded to bring the wheel to rest in (i) 2 minutes, and (ii) 18 revolution.

Answer 1

just used the formula and figured out hope calculation is correct

Answer 2

Answer:

Step-by-step explanation:

Definition of angular displacement:

An object rotating about an axis experiences an angular displacement  where u is positive for rotation that is counterclockwise and negative for rotation that is clockwise.

Definition of angular velocity and angular speed:

When a body rotates in an angular movement average angular velocity v avg during the course of time t equals to The body's (instantaneous) angular velocity is

ω=d∅/dt

Both v avg and v are vectors, and the right-hand rule of Fig. 10-6 specifies their directions. In the case of rotation in the clockwise direction, they are negative. The angular speed of a body is the size of its angular velocity.

Definition of angular acceleration:

The average angular acceleration of a body is equal to a avg if its angular velocity varies from v1 to v2 in the time interval t2 to t1

The body's (instantaneous) angular acceleration is

∝=dω/dt

Given:

constant speed=360 r. p. m

time= 2 minutes

distance covered by the object(s)=18

Find:

angular acceleration

Solution:

RPM= Revolution per minute

1 rpm = 2π/60 rad/s

360 rpm =( 2π*360)/60

360 rpm= 12π rad/s

ω=12π rad/s

$ω^{2}$=$ω^{2}$+∝t

t=2s

$ω^{2}$=$ω^{2}$+2∝s

0=144$π^{2}$+2∝*18*2π

2π=∝

ω=ω+∝t

0=12π+120∝

∝=π/10 rad/s

Hence angular acceleration(∝)=π/10 rad/s

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