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.

1 Answer
Feb 2, 2018

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