1. A force F applied to a cord wrapped around a cylinder pulley. The parell motor is 2 N m and the moment d'inèrcia is kg 1 m2, que es el acceleració angular del cilindre.
Conegut:
Parell (τ) = 2 N m
The moment of inertia (I) = 1 kg m2
Volia: The angular acceleration of the cylinder
Solució:
St = I α
St = net torque, I = moment of inertia, α = angular acceleration
Angular acceleration of cylinder :
α = Στ / I = 2 / 1 = 2 rad/s2
2. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of the force is 10 N, the radius of the cylinder is 0.2 m and the moment of inertia is kg 1 m2, What is the angular acceleration of the cylinder?
Conegut:
Força (F) = 10 N
Radius of cylinder (R) = 0.2 m
The moment of inertia (I) = 1 kg m2
Volia: The angular acceleration of the cylinder.
Solució:
τ = F R
τ = torque, F = force, R = radius of cylinder
Parell motor :
τ = F R = (10 N)(0.2 m) = 2 N m
St = I α
St = net torque, I = moment of inertia, α = angular acceleration
Angular acceleration of cylinder :
α = Στ / I = 2 / 1 = 2 rad/s2
3. A force F applied to a cord wrapped around a cylinder pulley. The magnitude of force is 10 N, the radius of cylinder is 0.2 m and the mass of cylinder is 20 kg m2,. What is the angular acceleration of the cylinder.
Conegut:
Força (F) = 10 N
Radius of cylinder (R) = 0.2 m
Mass of cylinder (M) = 20 kg
Es busca: Angular acceleration of cylinder
Solució:
τ = F R = (10 N)(0.2 m) = 2 N m
Moment d'inèrcia:
I = 1⁄2 MR2 = 1⁄2 (20)(0.2)2 = 1⁄2 (20)(0.04) = 0.4 kg m²2
Angular acceleration of cylinder :
α = Στ / I = 2 / 0.4 = 5 rad / s2
4. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The moment of inertia of pulley is 1 kg m2 and the radius of pulley is 0.2 m. What is the angular acceleration of the pulley. Acceleració per gravetat és de 10 m/s2.
Conegut:
Moment of inertia of pulley (I) = 1 kg m2
Massa del bloc (m) = 1 kg
Acceleració deguda a la gravetat (g) = 10 m/s2
pes (w) = mg = (1 kg)(10 m/s2) = 10 kg m/s2 = 10 N
Radius of pulley (R) = 0.2 m
Es busca: Acceleració angular
Solució:
Parell motor :
τ = F R = w R = (10 N)(0.2 m) = 2 N m
Moment d'inèrcia:
I = 1 kg m2
Angular acceleration :
α = Στ / I = 2 / 1 = 2 rad / s2
5. A 1-kg block hanging from a cord wrapped around a cylinder pulley. The mass of pulley is 20 kg and the radius of pulley is 0,2 m. What is the angular acceleration of the pulley and the caiguda lliure acceleration of the block. Acceleration due to gravity is 10 m/s2.
Conegut:
Mass of pulley (M) = 20 kg
Radius of pulley (R) = 0,2 m
Massa del bloc (m) = 1 kg
Acceleració deguda a la gravetat (g) = 10 m/s2
Pes (p) = mg = (1 kg)(10 m/s)2) = 10 kg m/s2 = 10 N
Es busca: the angular acceleration of the pulley and the free fall acceleration of the block.
Solució:
El parell de torsió:
τ = F R = w R = (10 N)(0.2 m) = 2 N m
El moment d'inèrcia de la politja del cilindre:
I = 1⁄2 MR2 = 1⁄2 (20)(0.2)2 = (10)(0.04) = 0.4 kg m²2
The angular acceleration of the pulley :
α = Στ / I = 2 / 0.4 = 5 rad / s2
The free fall acceleration of the block :
a = R α = (0.2)(5) = 1 m/s2
