Awheel of radius 0.38 m rotates in a clockwise sense about a fixed axle with negligible friction at an initial angular speed of 1.6 rad/s. the wheel’s mass of 14 kg is concentrated in its rim. you apply a clockwise torque to the rotating wheel by pushing on the rim tangentially with a constant force of 24 n.
find the wheel's angular speed, in radians per second, 0.13 seconds after you start pushing on the rim.

ωf = 2.19 rad/s

Explanation:

Newton's second law:

F = ma has the equivalent for rotation:

τ = I * α   Formula  (1)

where:

τ : It is the torque applied to the body.  (Nxm)

I :  it is the moment of inertia of the body with respect to the axis of rotation (kg*m²)

α : It is angular acceleration. (rad/s²)

Data

F = 24 N  : Tangential force

m : 14 kg : mass of the wheel

R = 0.38 m : radius of the wheel

Moment  of inertia of  the wheel

The moment of inertia of wheel is defined as follows:

I = m* R²

I = 14 kg*(0.38)²

I = 2.0216 kg*m²

Torque applied to the wheel

The Torque ( τ) applied to the wheel is defined as follows:

τ = F*d

Where:

F : Tangential force applied to the wheel

d : Perpendicular distance of the tangential force to the axis of rotation

τ = (24N)*(0.38 m)

τ = 9.12 N*m

Angular acceleration of the wheel  (α )

We replace data in the formula (1):

τ = I * α

9.12 = (2.0216) * α

α= 9.12 / (2.0216)

α = 4.5 rad/s²  

Kinematics of the wheel

We apply the equations of circular motion uniformly accelerated :  

ωf = ω₀ + α*t Formula (2)

Where:  

α : Angular acceleration (rad/s²)  

ω₀ : Initial angular speed ( rad/s)  

ωf : Final angular speed ( rad

t : time interval (s)

Data  

α = 4.5 rad/s²  

ω₀ =1.6 rad/s

t =  0.13 s    

We replace data in the formula (2):  

ωf = ω₀ + α*t

ωf = 1.6 + (4.5)*(0.13)

ωf = 1.6 + (4.5)*(0.13)

ωf = 2.19 rad/s

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

real, smaller and upside-down.   so the answer should be b.