I already figured out the answers to some but I need help with two more.
1) A disk with an initial angular velocity ω0 = 4.5 rad/s experiences a constant angular acceleration of α = 7.5 rad/s2 for time t = 15 s. Please answer the following questions.
ω0 = 4.5 rad/s
α = 7.5 rad/s^2
t = 15 s
Part (a) Write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters.
ω= ω0 + α*t
Part (b) Calculate the magnitude of the angular velocity of the disk in rad/s at time t.
117
Part (c) Write an expression for the magnitude of the angular displacement θ traveled by a point on the disk during the angular acceleration described in terms of the given parameters. Assume the point starts at an angular displacement of 0 radians.
Part (d) Calculate the magnitude of the angular displacement in radians traveled by a point on the disk during the acceleration described
I think I got it.
c) ω0 t + (0.5*α*t^2)
d) 911.3
Can you just double check this?
Part (c) Writing an expression for the magnitude of the angular displacement θ traveled by a point on the disk during the angular acceleration described in terms of the given parameters:
θ = ω0*t + (1/2)*α*t^2
Part (d) Calculating the magnitude of the angular displacement in radians traveled by a point on the disk during the acceleration described:
θ = 4.5*15 + (1/2)*7.5*(15^2)
θ = 67.5 + (1/2)*7.5*225
θ = 67.5 + 843.75
θ = 911.25 radians
Part (c) The expression for the magnitude of the angular displacement, θ, can be calculated using the formula:
θ = ω0 * t + 0.5 * α * t^2
Given the values:
ω0 = 4.5 rad/s
α = 7.5 rad/s^2
t = 15 s
Substituting these values into the formula:
θ = 4.5 rad/s * 15 s + 0.5 * 7.5 rad/s^2 * (15 s)^2
θ = 67.5 rad + 0.5 * 7.5 rad/s^2 * 225 s^2
θ = 67.5 rad + 0.5 * 7.5 rad/s^2 * 225 s^2
θ = 67.5 rad + 843.75 rad
θ = 911.25 rad
Therefore, the magnitude of the angular displacement traveled by a point on the disk during the described acceleration is 911.25 radians.
Part (d) The magnitude of the angular displacement traveled by a point on the disk during the acceleration described is 911.25 radians.
Part (a) Write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters:
The expression for the magnitude of the angular velocity (ω) at time t is given by the formula:
ω = ω0 + α*t
where ω0 is the initial angular velocity, α is the constant angular acceleration, and t is the time.
In this case, we have ω0 = 4.5 rad/s, α = 7.5 rad/s^2, and t = 15 s. Substituting these values into the formula, we get:
ω = 4.5 + 7.5 * 15
Part (b) Calculate the magnitude of the angular velocity of the disk in rad/s at time t:
To calculate the magnitude of the angular velocity at time t, we substitute the given values into the expression we derived in part (a):
ω = 4.5 + 7.5 * 15 = 4.5 + 112.5 = 117 rad/s
Therefore, the magnitude of the angular velocity of the disk at time t is 117 rad/s.
Part (c) Write an expression for the magnitude of the angular displacement (θ) traveled by a point on the disk during the angular acceleration described in terms of the given parameters. Assume the point starts at an angular displacement of 0 radians:
When a point on the disk undergoes angular acceleration, the angular displacement (θ) can be calculated using the formula:
θ = ω0*t + (1/2)*α*t^2
where ω0 is the initial angular velocity, α is the constant angular acceleration, and t is the time.
In this case, the point starts at an angular displacement of 0 radians (θ0 = 0). Substituting the given values into the formula, we get:
θ = 0 + (1/2) * 7.5 * 15^2
Part (d) Calculate the magnitude of the angular displacement in radians traveled by a point on the disk during the acceleration described:
To calculate the magnitude of the angular displacement, we substitute the given values into the expression we derived in part (c):
θ = (1/2) * 7.5 * 15^2 = (1/2) * 7.5 * 225 = 843.75 radians
Therefore, the magnitude of the angular displacement traveled by a point on the disk during the acceleration is 843.75 radians.