A uniform disc of moment of inertia 75 kg * m ^ 2 and radius of gyration 3 rates with an angula velocity of 2 rad s', Determine the (1) mass ( radius (14) angular imomentum and (|x) kinetic energy of the disc.
A cylinder of mass 65kg has a radius of gyration 0.8m the cylinder rotated by a belt at 4revolutions per second. Calculate the rotation
A uniform disc of moment of inertia 75 kg * m ^ 2 and radius of gyration 3 rates with an angula velocity of 2 rad s', Determine the (1) mass ( radius (14) angular imomentum and (|x) kinetic energy of the disc.
A cylinder of mass 65kg has a radius of gyration 0.8m the cylinder rotated by a belt at 4revolutions per second. Calculate the rotation
A torque 75 * 10Xm is applied to a circular solid disc grind when whose mass is 250 g and adius is 0.15m for 10s. Calculate the angula momentum and rotational kinetic energy of the wheel at the end of th
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To calculate various quantities related to rotational motion, we need to use the formulas related to moment of inertia, angular velocity, mass, radius, angular momentum, and kinetic energy.
For the first question:
Given:
- Moment of inertia (I) = 75 kg * m^2
- Radius of gyration (k) = 3 m
- Angular velocity (ω) = 2 rad/s
1. To find the mass:
The formula for moment of inertia is I = m * k^2, where m is the mass.
Rearranging the equation, m = I / k^2.
Substituting the given values, m = 75 kg * m^2 / (3 m)^2 = 75 kg.
2. To find the radius:
The radius (R) can be calculated using the formula R = k.
Substituting the given value, R = 3 m.
3. To find the angular momentum:
Angular momentum (L) is given by L = I * ω.
Substituting the given values, L = (75 kg * m^2) * (2 rad/s) = 150 kg * m^2/s.
4. To find the kinetic energy:
Kinetic energy (K) is given by K = (1/2) * I * ω^2.
Substituting the given values, K = (1/2) * (75 kg * m^2) * (2 rad/s)^2 = 150 J.
For the second question:
Given:
- Mass (m) = 65 kg
- Radius of gyration (k) = 0.8 m
- Angular velocity (ω) = 4 rev/s (1 revolution = 2π radians)
To find the rotation, we need more information, such as the time the cylinder rotates or the angle through which it rotates.
For the third question:
Given:
- Torque (τ) = 75 * 10^(-10) N*m
- Mass (m) = 250 g = 0.25 kg
- Radius (r) = 0.15 m
- Time (t) = 10 s
1. To find the angular momentum:
Angular momentum (L) is given by L = I * ω, where I is the moment of inertia and ω is the angular velocity. However, we need to calculate the angular velocity first.
The torque (τ) is related to angular acceleration (α) and moment of inertia (I) by the equation τ = I * α. Rearranging this equation to solve for α, we have α = τ / I.
The angular velocity (ω) can be found using the equation α = ω / t, where t is the time.
Combining these equations, we get ω = (τ / I) * t.
Substituting the given values, ω = (75 * 10^(-10) N*m) / (0.25 kg * (0.15 m)^2) * 10 s.
2. To find the rotational kinetic energy:
Rotational kinetic energy (K) is given by K = (1/2) * I * ω^2.
Substituting the given values for I and ω, K = (1/2) * (0.25 kg * (0.15 m)^2) * (ω^2 obtained from the previous step).
Note: Make sure to convert the final result into the desired units if needed.