Question

A typical ten-pound car wheel has a moment of inertia of about 0.35 kg⋅m2 . the wheel rotates about the axle at a constant angular speed making 65.0 full revolutions in a time interval of 5.00 s .

Answer 1

The angular acceleration of the car wheel can be calculated by dividing the net torque applied to the wheel by its moment of inertia.

Step-by-step explanation:

The angular acceleration of the wheel can be calculated using the formula:

Angular acceleration = (net torque) / (moment of inertia)

In this case, the net torque applied to the wheel is 95.0% of 200 Nm, which is 190 Nm. The moment of inertia of the wheel can be calculated using the formula:

Moment of inertia = (1/2) * m * r^2

Substituting the values given in the question, the moment of inertia is:

Moment of inertia = (1/2) * 2.00 kg * (0.180 m)^2 = 0.065 kg*m^2

Substituting the values into the formula for angular acceleration:

Angular acceleration = (190 Nm) / (0.065 kg*m^2) = 2923 rad/s^2

Answer 2

Final nswer:

In this case, the rotational kinetic energy of the rotating wheel is approximately 114.36 Joules.

Step-by-step explanation:

To find the rotational kinetic energy (K) of the rotating wheel, we can use the formula:

K = (1/2) * I * ω²

where:

• K represents the rotational kinetic energy,
• I represents the moment of inertia, and
• ω represents the angular speed.

Given that the moment of inertia (I) of the wheel is 0.35 kg⋅m², and the wheel makes 65.0 full revolutions in a time interval of 5.00 s, we need to find the angular speed (ω) first.

To find the angular speed, we can use the formula:

ω = (2π * n) / t

where:

• n represents the number of revolutions, and
• t represents the time interval.

Substituting the given values, we have:

ω = (2π * 65.0) / 5.00

Calculating this, we find:

ω ≈ 26.18 rad/s

Now we can substitute the values of I and ω into the formula for rotational kinetic energy:

K = (1/2) * 0.35 kg⋅m² * (26.18 rad/s)²

Simplifying this expression, we get:

K ≈ 114.36 J

Therefore, the rotational kinetic energy of the rotating wheel is approximately 114.36 Joules.

Your question is incomplete, but most probably the full question was:

A typical ten-pound car wheel has a moment of inertia of about 0.35 kg⋅m² . the wheel rotates about the axle at a constant angular speed making 65.0 full revolutions in a time interval of 5.00 s .

What is the rotational kinetic energy K of the rotating wheel?