A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian / s 2 is (π/x). Find the value of x.

Question

A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian / s 2 is (π/x). Find the value of x. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

ω i =(900/60) × 2 π=30 π rad / s , ω f =0, t =60 s ω f =ω i +α t ∴ α=(ω f -ω i / t )=(0-30 π/60)=-(π/2) rad / s 2 Here, -ve sign shows angular retardation.

Q. A wheel is rotating at $900$ r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian $/ s^{2}$ is $\frac{π}{x}$ . Find the value of $x$ .

$ω_{i} = \frac{900}{60} \times 2 π = 30 π r a d / s, ω_{f} = 0, t = 60 s$
$ω_{f} = ω_{i} + α t$
$∴ α = \frac{ω _{f} - ω _{i}}{t} = \frac{0 - 30 π}{60} = - \frac{π}{2} r a d / s^{2}$
Here, -ve sign shows angular retardation.

Q. A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian /s2 is xπ​. Find the value of x.

ωi​=60900​×2π=30πrad/s,ωf​=0,t=60s ωf​=ωi​+αt ∴α=tωf​−ωi​​=600−30π​=−2π​rad/s2 Here, -ve sign shows angular retardation.

Q. A wheel is rotating at $900$ r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian $/ s^{2}$ is $\frac{π}{x}$ . Find the value of $x$ .

$ω_{i} = \frac{900}{60} \times 2 π = 30 π r a d / s, ω_{f} = 0, t = 60 s$
$ω_{f} = ω_{i} + α t$
$∴ α = \frac{ω _{f} - ω _{i}}{t} = \frac{0 - 30 π}{60} = - \frac{π}{2} r a d / s^{2}$
Here, -ve sign shows angular retardation.