Question

A wheel originally rotating clockwise at 98 rad/s speeds up to 125 rad/s while turning through 628 radians. Assume a constant rate of acceleration. The wheel is 1.3m?

A) Find the magnitude of the angular acceleration of the wheel

B) Calculate the initial angular speed of the wheel in units of rotations.

C) Calculate the centripetal acceleration, the tangential acceleration and the magnitude of the total acceleration of the wheel when it just starts to speed up (at t=0s) for a point on the rim of the wheel.

Answer 1

See the explanation below

Explanation:

Aply the equation (rotational)

`omega^2=omega_0^2+2alphatheta`

The initial angular velocity is `omega_0=98rads^-1`

The final angular velocity is `omega=125rads^-1`

The angle is `theta=628rad`

Therefore,

The angular acceleration is

`alpha=(omega^2-omega_0^2)/(2theta)=(125^2-98^2)/(2*628)`

`=4.79rads^-2`

The initial angular velocity is `omega_0=98rads^-1`

`=98/(2pi) "turns per sec"`

`=98/(2pi)*60 " rpm"`

`=935.8" rpm"`

The radius of the wheel is `r=1.3m`

The centripetal acceleration is

`a_c=romega_0^2=1.3*98^2=12485.2rads^-2`

The tangential acceleration is

`a_T=alphar=4.79*1.3=6.23ms^-2`

The magnitude of the total acceleration is

`a=sqrt(a_C^2+a_T^2)=sqrt(12485.2^2+6.23^2)=12485.2`